How does Hale's speech express a message from the playwright?

The speech you are referring to occurs in act 4 once Hale's character has evolved to the point that he regrets his involvement in the witch hysteria that has stricken Salem. His speech reads as follows:

HALE: (To Elizabeth.) Let you not mistake your duty as I mistook my own. I came into this village like a bridegroom to his beloved, bearing gifts of high religion; the very crowns of holy law I brought, and what I touched with my bright confidence, it died; and where I turned the eye of my great faith, blood flowed upon it. Beware, Goody Proctor—cleave to no faith when faith brings blood. It is mistaken law that leads you to sacrifice. Life, woman, life is God‘s most precious gift; no principle however glorious may justify the taking of it. I beg you, woman—prevail upon your husband to confess. Let him give his lie. Quail not before God‘s judgment in this, for it may well be God damns a liar less than he that throws his life away for pride. Will you plead with him? I cannot think he will listen to another.

Hale explains to Elizabeth Proctor that he was wrong in his original intent. He has seen the trauma and suffering caused by the witch hunt, and he feels that he must help to put an end to it. He warns her against devoting herself to a faith that requires the believers to cause suffering to others. He does not think faith should result in bloodletting. Hale says that a true religion would not ask a believer to take the life of another. He urges Elizabeth to convince her husband John to confess (even though he'd be lying) to being a witch to save his life. John does not do so, thinking he cannot live with the sin of lying on his soul, and so he is put to death.
It is well-known that Arthur Miller wrote The Crucible during the McCarthy era in the 1950s to draw parallels between that era and the Salem witch trials. Here, the voice of the playwright can be heard warning the audience not to misplace their faith, out of fear, in a vengeful "witch hunt" that destroys lives and reputations. Like religion in the play, the government should not be trusted blindly; we should question its motives if it leads to citizens turning on one another, reveling in one another's suffering, or seeking to ruin or take away lives.

Compare and contrast "Alone" and "Spirits of the Dead" by Edgar Allan Poe.

Both of these poems are about the experience of feeling alone, solitary. But the first, "Alone," seems to focus upon the speaker's formative process, and the uniqueness of it—the fact it is different from that of other people. "Spirits of the Dead," on the other hand, is concerned more with the universal experience of those who are facing death, and their feeling of being cut off from the emotions that animate people who are either not at the end of life or not contemplating the end.
In reading Poe's "The Poetic Principle" I find him leaning towards valuing verse more for its sensory qualities—as a kind of music, in fact—than for its meaning. He defines the concept of truth as somehow opposed to the poetic:

In enforcing a truth, we need severity rather than efflorescence of language. We must be simple, precise, terse. We must be cool, calm, unimpassioned. In a word, we must be in that mood which, as nearly as possible, is the exact converse of the poetical.

Later in the essay he adds that,

To recapitulate, then:—I would define, in brief, the Poetry of words as The Rhythmical Creation of Beauty. Its sole arbiter is Taste. With the Intellect or with the Conscience, it has only collateral relations. Unless incidentally, it has no concern whatever either with Duty or with Truth.

I include these quotes from Poe's aesthetic writings because I believe the two poems selected for comparison both illustrate this primacy of sound and rhythmical beauty over actual "truth." The general impression of "Alone" is one dominated by the flowing, languid quality of the words, and the actual meaning of why the speaker feels this way is somehow in the background, less important than the hypnotic wording, a kind of melancholy melody that continues to haunt us after we have read the poem. In "Spirits of the Dead," the meaning of the poem, to me, seems more concrete, though still showing the centrality of a musical feature in Poe's verse. In the contemplation of death the speaker is alluding, much like Hamlet, to the mystery of what follows death. Of the "breath of God" he says,

How it hangs upon the trees,
A mystery of mysteries!

But beyond the level of not knowing, the speaker also views death in the most negative terms. Of the stars he says:

But their red orbs, without beam,
To thy weariness shall seem
As a burning and a fever
Which would cling to thee for ever.

Despite the differences in theme—the one poem dealing with the formative elements of the speaker's character, and the other dealing with his end-of-life thoughts, what links these poems, as well as their preeminently musical quality, is a pessimistic feeling, one of sorrow or negation. "Alone" abruptly ends with the description of a cloud as "a demon in my view—". That it ends with a dash leaves a feeling of a life truncated, much as Poe's own life actually was.

Both poems contain a somber tone and include supernatural elements. Edgar Allan Poe’s tragic backstory is woven into his poetry, and these two poems utilize a dark tone to express his complicated feelings about life. Poe uses these poems to wrestle with the pain he has experienced, whether it’s grieving over his dead wife or reminiscing about his youth. Also, each poem contains a reference to the supernatural, such as heaven, demons, and spirits. This was common during the Gothic literature period, which influenced Poe’s melancholic writing style.
“Spirits of the Dead” addresses the death of Poe’s wife, while “Alone” is centered on Poe’s past. In terms of structure, “Alone” is a lyric poem with eleven rhyming couplets, while “Spirits of the Dead” is free verse with different rhyming patterns.
https://poets.org/poem/spirits-dead

https://www.poemhunter.com/poem/alone-5/

What emotions do the images starting in line 19 of "The Guitar" ("Hot southern sands") convey to the reader? What theme or message is Lorca making in this poem?

Lorca's poem "The Guitar" is meant to imitate the sounds of a guitar and to use that sound and the image of a guitar to evoke the way in which life does not always fulfill one's hopes and yearnings. The poem presents a series of images that metaphorically represent the ways in which the guitar cries for what it cannot have but desperately wants. 
Lines 19-20 begin a series of images and metaphors about what the guitar cries for. These lines read, "Hot southern sands/ yearning for white camellias." This image is of a desert that yearns for lush flowers. Later lines present other objects yearning for what they cannot have, such as an arrow crying for a target, evening yearning for morning, and a bird that dies on the branch. The bird, a symbol of innocence, meets death instead of enjoying life. Then, Lorca compares a guitar to a heart that is hurt by "five swords," or the five fingers that play it. While the guitar wails for things it cannot have, it must suffer being wounded by five fingers. The emotions conveyed in these lines are suffering that arises from unrequited hopes, and the theme of the poem is that life is filled with this type of mournful longing. 

In "Salvage the Bones" by Jesmyn Ward, why is the tenth day titled as "In the Endless Eye"?

The eye of the storm is actually the calmest part of a hurricane storm. Most of the heavy and tempestuous winds are deflected from the eye of the hurricane by the Coriolis Effect. The Coriolis Effect basically describes the deflection of air as it moves from high to low pressure in the Northern Hemisphere and the Southern Hemisphere.
So, the tenth chapter of the book refers to the peace before the storm (or before Hurricane Katrina makes landfall). Since the eye of the storm is the calmest part of the hurricane, this chapter describes the surreal, peaceful moments before the hurricane makes land. In the chapter, some of the houses have been boarded up, and the families have left; only some families, like the Batiste family, are staying put. In the woods, no animals can be seen. There is at once a deadly calm to everything as well as a sense that powerful forces will soon bear down on the family.
The "endless eye" possibly refers to the endless wait (under falsely calm conditions) for the hurricane's arrival. In this chapter, the conflict between Manny and Esch foreshadow the fierceness of the approaching storm. While the family makes preparations for the storm, they are, figuratively, in the "eye of the storm," where everything is supposedly calm. However, the calm center is flanked by the gusty winds and copious raindrops that will soon batter the land as the hurricane hits.
http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/hurr/stages/cane/eye.rxml

What is the point of view of "The Adventure of the Speckled Band" by Sir Arthur Conan Doyle, and who is the narrator?

The point of view in "The Adventure of the Speckled Band," as in other Sherlock Holmes stories, is first person limited. Specifically, the narrator, Dr. John Watson, is a first person witness narrator: he is telling a story which he has personally witnessed, rather than one that has been told to him by someone else. However, he is not the protagonist telling his own story but rather a character close to the main character whose function is to observe that character at work and record the details of his cases.
The structure of Watson's narration relies upon the idea that he is writing these stories for publication in The Strand. As such, we could argue that Watson's perspective is not so much limited as it is unlikely to be completely accurate; he is editing his story for a specific audience. This story, also, is said to have happened "in the early days of my association with" Sherlock Holmes, so it does not have the immediacy it might have if the narrator was recounting recent events. In considering first person points of view, we should assess how far the narrator is reliable or unreliable and how much he is likely to understand about the events he describes. In Watson's case, he is a witness to the story, but the distance of time may have blurred the true facts. He is also, for a period in this story, retelling the words of someone else: Helen Stoner.
While the frame narrative of the story is narrated by John Watson, there is also a section within this story which is narrated by Helen Stoner, as she tells her own story. Interjections from Holmes and Watson keep this narrative tethered to the frame narrative, told by Watson, but at these points, Watson becomes a narrator retelling somebody else's words.

Dr. John Watson, Sherlock Holmes's friend and assistant, narrates "The Adventure of the Speckled Band" in first person. This is the typical technique Conan Doyle adopts for the Holmes stories, although he does write a handful either in the third person or in Holmes's own voice. First person narration is generally well-suited to the mystery genre because (in contrast to, for example, third person omniscient) its perspective is necessarily limited; the narrator (usually) does not know any more than the reader does, which is handy for a genre that relies on delivering a surprise ending. This is also why Watson generally makes for a more compelling narrator than Holmes; Holmes's brilliance as a detective requires him to "know" the mystery's solution well before the ultimate reveal, which could obviously spoil the ending for readers. Watson, by contrast, is just as in the dark as Conan Doyle's readers, though he often adds to the story's suspense by observing and interpreting Holmes's behavior (e.g., "I had never seen my friend’s face so grim or his brow so dark as it was when we turned from the scene of this investigation").

In Cofer's "American History," what story details reflect the writer's background?

Judith Ortiz Cofer is from Puerto Rico and so is her protagonist, Elena. Some details in the story that reflect this common heritage revolve around music, language, food, and certain behaviors. First, the music played in El Building comes from Puerto Rico. The following passage demonstrates the writer's experience with how Puerto Ricans use music to help them cope with the struggles of life:

"El Building was like a monstrous jukebox, blasting out salsas from open windows as the residents . . . tried to drown out whatever they were currently enduring with loud music."

Next, the use of language can reflect an individual culture. For instance, slang terms can help to identify one person with a particular group. Elena's mother tells her that she is "Enamorada," which is a term used to identify a Puerto Rican girl who is "stupidly infatuated." An equivalent turn of phrase akin to "enamorada" for today's teens might be that Elena is "crushing" on Eugene. Since the writer understands the language and slang used in the Puerto Rican culture, such words or phrases are used in her story about a girl not unlike herself.
Third, Cofer must know what it is like to go to a high school where African-American girls joke about a person's background. They tease Elena about eating rice, beans and pork chops. Specifically, the mean girls yell at Elena, "Pork chop, pork chop, did you eat your pork chop?" Cofer also mentions specifically how jealous Elena is that the African-American girls can skip rope better than she can. These deep feelings of inferiority seem to connect Cofer to her protagonist in specific ways only known to one who could have experienced the same.
Finally, when Elena walks home after hearing that President Kennedy was assassinated, Cofer explains how Puerto Ricans show respect for the dead in El Building. First, there is no music spilling out of the building; next, the unemployed men aren't out front complaining about life; then, Elena's mother asks her to go to church with her that evening to show respect for the fallen president. This behavior of the Puerto Rican people show respect for the president they loved. Through Elena, Cofer demonstrates the intricacies of life as a Puerto Rican immigrant in the 1960s. 

What is the significance of homosociality in "The Beach of Falesa"? How does it contribute or conflict with the portrayal of imperial activity?

In sociology, a homosocial relationship is one between two people of the same sex which is not of a sexual or romantic nature. Most people these days are familiar with the word "bromance," which means much the same thing. The homosocial relationship at the heart of "The Beach of Falesá" is that between Wiltshire and Case. I would like to suggest that it is directly related to the imperialist theme that Robert Louis Stevenson wishes to convey in the story.
It is interesting to note that Stevenson conceived "The Beach of Falesá" as an example of literary realism. He sought to portray life in the South Sea islands with complete fidelity to the reality of everyday life, warts and all. Among other things, this meant showing, without prejudice, the effects of British colonial rule upon the indigenous population.
The relationship between Wiltshire and Case is arguably one that could not have happened had they remained in England. Their personalities are different, for one thing. Yet, their destinies collide in the setting of a remote tropical outpost of the British Empire, the South Sea island of Falesá. The empire has brought them together. Their homosociality is a product of colonialism and their respective roles in it. Despite their differences in personality and temperament, the two men are brought together by shared ties of race and culture. Naturally, they gravitate toward each other.
Wiltshire and Case are traders. As such, they have come to Falesá to exploit the opportunities presented to them by colonial commerce. As well as race and culture, then, they are drawn together by economic necessity. Though they are rivals competing for the same business, they do at least have a mutual understanding.
Despite the ostensible bond between them, the homosocial relationship between Wiltshire and Case is fraught from the outset. As their relationship emerged out of a social context of fraud, exploitation, and cutthroat competition, it is not surprising that their connection develops along similar lines. The fateful acquaintance of the two men is a microcosm of what is happening in the world around them.
For all of Case's superficial bonhomie and good will, he is too experienced at the game of colonialism not to spot an opportunity for domination and control when he sees one. Case starts to treat Wiltshire the same way he treats every native he has ever come across: a sucker to be cheated and exploited. He is also a master at using superstition to his advantage, a practice to which even white colonialists like Wiltshire are not immune.
When Wiltshire realizes he has been had, his relationship with Case is effectively over. The bonds between them have been irreversibly severed. Additionally, Wiltshire's love for Uma has given him a new perspective on life, one no longer dominated by colonial preconceptions and prejudices. His connection to Case was purely skin deep, based as it was on superficial similarities of race, gender, and occupation. In throwing off the shackles of homosociality, Wiltshire has embraced his humanity and cast off his accretions, which led to his being suckered into Case's cruel world of dark dishonesty.