How did American leaders convince ordinary people to join the militias to fight in the Revolutionary War?

The arguments were different based on where the militia was located. In the South, after Banastre Tarleton executed Americans, and the British army promised freedom to any slave who assisted their cause, fighting for the colonial militias was a way to preserve the social order of slavery or a way to avenge those deaths caused by the British killing prisoners of war.  
Throughout the colonies, the patriots fought in order to remove the invading British armies. They fought to defend their homes. Few soldiers were so touched by the tax issues of the day to make it their main motivation for fighting; however, many had to face some kind of British rule that they disliked.
The British also used German Hessians—these mercenaries were considered the most vicious in all of Europe. Many patriots fought because they thought that the British were treating the American colonies as occupied territory rather than land occupied by British subjects. Many preachers even called it "God's work" to defend the natural rights of the colonists by fighting against British rule.  

Why did Daito have to die?

The answer to your question is that Daito was a threat to IOI. In fact, all five of the gunters at the top of the Scoreboard were considered a threat to IOI. The organization's main goal was to annihilate these threats to their dominance.
In chapter 30, the text tells us about Wade hacking deep into the Sixers' private database. He comes across five folders enclosed in what is called a Threat Assessments folder. The five folders include personal information about Parzival, Aech, Shoto, Daito, and Art3mis.
Wade discovers that IOI has been spying on Art3mis and Shoto. Because IOI owns hundreds of local telecom companies, it is effectively the largest Internet service provider in Wade's world. From this formidable position, IOI has been able to keep Art3mis' home under surveillance. Wade learns that Sorrento was planning to abduct both Shoto and Art3mis (in real life). Once the two were in IOI's power, Sorrento was going to force them to help IOI open the Third Gate. After the Third Gate was breached, IOI would simply "dispose" of both gunters.
The only reason Parzival/Wade has not been caught is because he has taken the trouble to lease a private, direct fiber-optic connection to OASIS (the Internet in Wade's world).
So, we can see that Daito had to die because he was considered a threat to IOI. The organization had targeted all five gunters for death.

How did the Depression challenge the traditional belief of Hoover and other Americans in “rugged individualism”?

Herbert Hoover first coined the expression "rugged individualism" in a speech on the campaign trail in the 1928 presidential election. With this phrase, he articulated a long-standing American tradition, almost a civic religion, based upon a passionate belief in the value of hard work and self-reliance in which people looked to themselves to get ahead in life, instead of relying on the state to support them.
Rugged individualism certainly caught the attitude of the times. With the American economy booming and the good times seemingly set to stay, Hoover's classic statement of conservative moral and economic philosophy attained dominance in the marketplace of ideas.
However, with the onset of the Great Depression, all that changed. There had been economic depressions before, but none quite like this. In the face of this unprecedented downturn in the American economy, the whole concept of rugged individualism seemed woefully inadequate. At best, it was widely perceived as naive and unrealistic; at worst, it appeared to display a heartlessness toward the millions of impoverished Americans now struggling to eke out an existence against the backdrop of an economy in free fall. In the minds of many people, rugged individualism was now exposed as a sham; simply a nice way of describing greed and rampant self-interest.
Yet, despite all this, Hoover still clung stubbornly to the old faith. There is little evidence to suggest that he ever once felt rugged individualism to be mistaken or in any way out of date. This is not altogether surprising. For Hoover, rugged individualism was not some abstract idea; it was an abiding creed by which he had lived his whole life.
At the same time, Hoover, though undoubtedly committed to his guiding principle, did not display a narrow, ideological commitment. In his famous speech, he openly acknowledged that there was sometimes a need for increased government involvement in the economy. It all depended on the circumstances. However, Hoover also made it clear that those circumstances must be truly exceptional, such as those arising during the First World War.
The Great Depression, however, was a different matter entirely. There was no need, thought Hoover, for a fundamental shift in American economic policy and its underlying values. However, as the country plunged further into economic catastrophe, Hoover finally heeded a growing chorus of disapproval with the prevailing approach and agreed to sanction increased federal aid for the hard-pressed states.
Even so, the sums made available proved totally inadequate for the sheer scale of the task. Ironically, the problem was made worse by the actions of Republican state governors and state legislatures. Many of them refused to spend the sums they had been granted, true believers in the faith of rugged individualism.
https://millercenter.org/president/hoover/domestic-affairs

What is the significance of the nude dancer in "Battle Royal"?

The significance of the dancer is two-fold. First, she serves as a way to make the boys in the ring even more uncomfortable than they already are. The white men have designed an event to make all of the black characters feel small, unimportant, and less worthy as people. The nude woman serves as a tool that the white men use to further dehumanize the boys; however, the nude woman is also important at showing how the white men view anybody that isn't a white man. The men do not see the nude woman as any more worthy of their respect than they give the black boys in the ring. It is blatant sexual objectification on their part. They have reduced the woman to nothing more than the sum of her feminine, attractive parts. Her feelings do not matter to the men. Her thoughts do not matter. She is an attractive, nude woman that is there for their sexual titillation. She is an object to be used and abused, and that is why some of the men even begin attempting to grope her.

As the dancer flung herself about with a detached expression on her face, the men began reaching out to touch her. I could see their beefy fingers sink into her soft flesh. . . It was mad. Chairs went crashing, drinks were spilt, as they ran laughing and howling after her. They caught her just as she reached a door, raised her from the floor, and tossed her as college boys are tossed at a hazing, and above her red, fixed-smiling lips I saw the terror and disgust in her eyes, almost like my own terror and that which I saw in some of the other boys.

Just like the boys, the nude woman has been dehumanized so that the powerful white men might have some "fun."

The narrator—along with some of his class mates—is forced to participate in a series of humiliating, degrading activities at what he thought would be his high school graduation speech. He's an unwilling participant in what turns out to be an evening's entertainment for a roomful of baying, drunken white men. Part of that entertainment involves an erotic dance performed by a nude lady with an American flag tattooed on her stomach.
The significance of the dance is that the noble values represented by the flag are distorted by the evening's sordid events. The flag is supposed to represent liberty above all else, and yet the tawdry, sleazy spectacle that unfolds is an attack on liberty, exploiting the young African American boys as well as the exotic dancer. Their freedom is compromised as they are part of groups in society that effectively have no power.

What are the words Charlotte used to make the story seem scary?

There are eerie and intimidating passages throughout Jane Eyre. One section that could be deemed scary is the opening of chapter 28. This chapter occurs right after Jane's attempted wedding with Mr. Rochester. When at the alter, Jane found out that a legal marriage could not happen between them, because Mr. Rochester was already married. His wife, Bertha Mason, went insane. Nonetheless, it was practically impossible for Rochester to get a legal divorce from his wife at this time. He was stuck with her until her death. She lived, with a personal servant, upstairs in Rochester's mansion.
Rochester tries to apologize to Jane, explaining why he didn't feel his marriage to Bertha counted as a real marriage anymore. He even tries to convince her to run away with him to some place where they could live as though they were husband and wife. Jane, however, is unhappy with living out only the appearance of marriage. She does not want to be Mr. Rochester's mistress—she wants to be his wife.
Though she claims she forgives him, Jane makes the decision to leave Rochester's mansion. Since she cannot be his wife, she does not think it is proper that she continue living in the same house. Chapter 28 picks up two days later. Jane has been traveling in search of some other place to live in work. (This is particularly challenging for a single, unmarried woman in the 19th century.) Jane explains her situation:

The coach is a mile off by this time; I am alone. At this moment I discover that I forgot to take my parcel out of the pocket of the coach, where I had placed it for safety; there it remains, there it must remain; and now, I am absolutely destitute. . . .

Jane's solitude is scary in this passage. She has no one to help her and no money or personal items, since she left her bag behind on the horse and carriage. Next, she explains her environment:

There are great moors behind and on each hand of me; . . . The population here must be thin, and I see no passengers on these roads: they stretch out . . . white, broad, lonely; they are all cut in the moor, and the heather grows deep and wild to their very verge. . . . I struck straight into the heath; I held on to a hollow I saw deeply furrowing the brown moorside; I waded knee-deep in its dark growth; I turned with its turnings, and finding a moss-blackened granite crag in a hidden angle, I sat down under it. (chapter 28).

In this passage, Jane is wandering in a moor, which is known for having only low-growing vegetation. In other words, the lands are vast and open, without any large trees. This adds to the sense of Jane's loneliness. Words such as "wild," "moss-blackened," "lonely," and "dark growth" show the eeriness of this setting. In this huge, open area, Jane finds a piece of granite that she can take shelter from the weather under. However, she is still unhappy, unsure of what to do, and uncomfortable:

I had a vague dread that wild cattle might be near, or that some sportsman or poacher might discover me. If a gust of wind swept the waste, I looked up, fearing it was the rush of a bull; . . . Finding my apprehensions unfounded, however, and calmed by the deep silence that reigned as evening declined at nightfall . . . . I had only listened, watched, dreaded . . . What was I to do? Where to go? Oh, intolerable questions, when I could do nothing and go nowhere!(chapter 28)

Jane continues to be uncomfortable, despite the fact that she has found a spot of shelter from the wind. (Since there were no trees, not much blocked the wind. It would have been very cold and uncomfortable for Jane in this environment, especially since she has no extra clothing with her, since she left her bag on the coach.) Words such as "vague dread," "fearing," "deep silence," "nightfall," "dreaded," and "intolerable," "nothing," and "nowhere," show the fear that Jane had in this situation. Jane's situation is extremely bleak at this moment. Many of these words make Jane's situation seem scary.

How does Jackson describe the black box and the slip of paper in "The Lottery?"

The black box used for the annual lottery drawing was in dilapidated condition because it was so old. Shirley Jackson describes it as follows.

The black box grew shabbier each year: by now it was no longer completely black but splintered badly along one side to show the original wood color, and in some places faded or stained.

Mr. Summers, who is in charge of the lottery drawings, keeps asking for the villagers to present him with a new box, but he never gets his wish. This suggests that the people are secretly hoping that the lotteries will come to an end when the box becomes useless. If they were to chip in to provide a brand-new box, it would be tantamount to voting to continue the lottery drawings for another hundred years or so. They obviously loathe the black box which symbolizes the horrible final event they are all too familiar with. When Mr. Summers asks for some help in holding the box

...there was a hesitation before two men. Mr. Martin and his oldest son, Baxter. came forward to hold the box steady on the stool while Mr. Summers stirred up the papers inside it. 

One of the papers contains a black spot. There will be two drawings. The first will determine the family selected for the second drawing. The same black spot will be placed back in the black box along with blank slips to total the number of members in the chosen family. Shirley Jackson describes the fatal slip when Bill Hutchinson forces it out of his wife Tessie's hand.

It had a black spot on it, the black spot Mr. Summers had made the night before with the heavy pencil in the coal company office.

Only the Hutchinsons participate in the second drawing. They are Bill, Sr., Tessie, Bill, Jr., teenage Nancy, and little Davy. All the other slips are allowed to blow away in the wind so that there would be no chance of any member of the selected family secretly pocketing a blank slip to show in case he or she had gotten the black spot. Tessie, it would seem, might be capable of doing something like that in order to avoid her fate. 
Although the black box seems terribly old, it is not the first one to be used for these annual ceremonies. 

There was a story that the present box had been made with some pieces of the box that had preceded it, the one that had been constructed when the first people settled down to make a village here.

It is the weight of tradition that keeps these simple people from abandoning their lottery. The children cannot escape from the tradition because they are indoctrinated at the earliest possible age. Little Davy Hutchinson represents the coming generation. Although he cannot be more than two years old, he is being taught how to draw the slip of paper that will doom one member of his family, and then how to draw the slip that could have easily resulted in his being stoned to death by his mother, father, big sister, older brother, and some three hundred of his family's friends and neighbors. 
 
 

What comparisons between Macbeth and the story of Achilles can be made?

If we look first at Macbeth and Achilles, we can say that they are both great warriors. Because he is the son of a goddess (Thetis) and was dipped in the River Styx, Achilles is virtually unbeatable in battle. As Macbeth opens, we learn of Macbeth's great feats in battle:

For brave Macbeth—well he deserves that name—
Disdaining fortune, with his brandished steel,
Which smoked with bloody execution,
Like valor’s minion carved out his passage
Till he faced the slave;
Which ne'er shook hands, nor bade farewell to him,
Till he unseamed him from the nave to th' chops,
And fixed his head upon our battlements.

In other words, Macbeth courageously killed many men to defend Duncan's throne, including one he chopped in half.
Both Macbeth and Achilles kill a royal. Macbeth kills King Duncan, and Achilles kills Hector, a prince who is heir to the Trojan throne. Both Macbeth and Achilles also behave dishonorably. Macbeth murders Duncan when Duncan is a guest at Macbeth's home, which violates all the rules of hospitality in his society. Macbeth is supposed to do everything he can to protect his guests, not kill them. Likewise, Achilles dishonors Hector by dragging his body around behind his chariot after he has killed him (though he does later allow a funeral for Hector).
Both men cause damage to their countries through their own weaknesses. Macbeth's weakness is his ambition, and Achilles's weakness is his pride and anger. Macbeth ends up bringing misery to Scotland by being overly ambitious, which leads him to become a tyrant. Malcolm, the rightful heir, brings an invading army to the country to win back the throne, plunging Scotland into war. Achilles almost deserts his countrymen, leaving them in danger of losing the Trojan War, because of his pride and rage.
Because Achilles will not fight, his best friend Patroclus dons his armor and is killed in battle; it is because of Achilles's pride and rage that his friend dies. Likewise, Macbeth has his good friend Banquo murdered because of his ambition: he is afraid Banquo knows too much and will cause him to lose the throne.
Stepping back a bit from the two main characters, it is notable that the story of Macbeth and the story of Achilles are both influenced by a supernatural element. A prophecy from the three witches, who are supernatural creatures, leads Macbeth to his bloody path, though he always had a choice to take a different path. A supernatural prophecy also surrounds Achilles, and it offers him two choice in life. He will either have glory and a short life or no glory and a long life:

For my mother Thetis the goddess of the silver feet tells me
I carry two sorts of destiny toward the day my death.
Either, if I stay here and fight beside the city of Trojans,
my return home is gone, but my glory shall be everlasting;
but if I return home to the beloved land of my fathers,
the excellence of my glory is gone, but there will be a long life
left for me, and my end in death will not come to me quickly.

Both Macbeth and the story of Achilles are exciting, violent tales with supernatural elements (the gods, such as Zeus, are always getting involved with Achilles, as the witches do with Macbeth). Each story examines the character flaws of two brave warriors, though Macbeth's flaw are darker and more damaging.