Why is it risky for the sniper to smoke right now?

The Republican sniper is located on a rooftop near the O’Connell Bridge in the war-torn city of Dublin, where the Republicans and Free Staters are waging a civil war. Given the fact that the sniper is in a war zone and the sun is rapidly going down, smoking a cigarette could easily give away his position to an enemy sniper and make him a target, which is exactly what happens.
At the beginning of the story, the Republican sniper quickly eats his sandwich, takes a sip of whiskey, and lights a cigarette. Almost immediately, a bullet from an enemy sniper positioned on the opposite roof strikes the parapet near the Republican sniper. Either the spark from the match or the smoke from the cigarette attracts the enemy sniper's attention, which gives away the Republican sniper's location. The Republican sniper is then forced to trick the enemy sniper into believing that he is dead in order to survive.

In "The Sniper" by Liam O'Flaherty, it is too risky for the sniper to smoke because the flash from his match could reveal his location to his enemies.
In the story, we learn that the Republicans and the Free Staters are at war. The sniper is a Republican, and he is keeping watch on a rooftop. He is ravenous and soon devours a sandwich hungrily. We get the idea that he is ready for action and impatient for the fighting to begin.
After eating, he takes a gulp of whiskey from his flask and then debates whether he should chance a smoke. Instinctively, he knows that his enemies are keeping watch as well. Because it is night, a flash from his match would draw attention to his position. So, it would be a risk to light up.
In the end, he decides to take the risk. His risk, however, is rewarded by an incoming bullet. The sniper ends up having to snuff out his cigarette. Although irritated, he has no choice but to return to the business of war.

What is chemcial equilibrium?

Living things carry out many chemical reactions in order to stay alive. A chemical reaction occurs when chemical bonds are made or broken between atoms. 
The molecules that take part in a chemical reaction are known as reactants and the final molecules that form as a result of the chemical reaction are known as products. Chemical reactions are reversible so that reactants in the forward reaction become products in the opposite reaction. 
When the amount of reactants and products do not change, one can describe this state as chemical equilibrium.
An example of a reversible reaction is when two molecules of hydrogen and one molecule of oxygen combine to form two molecules of water. In this reaction, the reactants are hydrogen and oxygen and the product is water. In the reverse reaction, water can break down into hydrogen and oxygen. In the reverse reaction, water is now the reactant and the products are hydrogen and oxygen.
If these reactions are occurring at the same rate, chemical equilibrium will occur. At equilibrium, the relative concentrations of both the reactants and products do not change.
https://www.thoughtco.com/chemical-equilibrium-606793

What are the themes of the play Words and Music by Samuel Beckett?

There are a couple of key themes worth considering in a discussion of Beckett's radio play Words and Music, written in 1961 and broadcast the following year. (Let us be sure not to confuse these with the themes and subthemes within the narrative itself: in the play, Croak, the main character, proposes several themes for the diversion of the small party, like Love, Age, the Face, and so on. However, I do not think that is what you are asking about. I believe your question is about Beckett's themes, not the character's proposed themes in the story.)
Let us talk about some of the important themes that this play brings up.
The elements of consciousness
The concept of the play, in part, is that Croak invites two minstrels, Joe (Words) and Bob (Music)—two characters who are often at odds—to entertain him in the hope that they will become friends. You could say that there are three characters in the play.
Some critics hold that these "characters" are only symbolic. They represent different parts of human consciousness. All of us, as human beings, have many different elements to our own consciousnesses—we have different ways to process information and different ways to express ourselves. There is a part of the brain that ignites when you are listening to classical music or walking through an art museum that is different than the part you might use when having an in-depth conversation with a friend, for instance. Beckett plays with this idea in the play, leaving us to wonder whether Words and Music are actual people or whether they are figurative.
The fallibility of man and the struggles of a creative life
Croak ("the poet"), our main character, despairs at his inability to create all of the art he dreams of. He can hear music in his head, but he cannot necessarily translate that beauty to the page.
He has tried and occassionally failed to write the way he wants to. He chides himself for his weakness, and he challenges (and even bullies) Words and Music—an expression of his own frustration.
The challenges of self-expression
We cannot express ourselves in words alone. Words are never enough. This is a theme that runs through Beckett's canon. Words are sometimes too much, and other times they can not be enough.
Music wins over Words in this play. Beckett has talked about this in interviews, and he has dealt with this theme in many of his works: there are ideas that cannot be spoken or written, and there are concepts so ephemeral that they are better expressed in musical form.

Is Vera's practical joke funny or cruel in "The Open Window" by Saki?

Vera's practical joke is cruel.
Admittedly, Nuttel is a stranger who has been more or less foisted on the Sappleton family by his sister, who apparently wanted to get rid of him. He seems to bore Mrs. Sappleton, who can barely suppress a yawn when he starts to talk to her. He appears to talk too much about his illness and its symptoms.
One can understand, therefore, why Vera, who has been left with this unfortunate guest on her hands, would want to get rid of him. Nevertheless, the way she choses, while ingenious, is nevertheless cruel.
Nuttel is in the country at the Sappleton house for a nerve cure. He appears to suffer from extreme anxiety. Vera plays on this with a false story that leads him to believe he is seeing ghosts. He flees the house in terror. The family is rid of an unwanted guest, but we can only imagine that, by playing on his weakness, Vera has made his condition worse.
It is generally considered cruel to find a person's weakness or vulnerability and use it against them. This is sometimes called "hitting below the belt line."

The answer, however, will depend on your worldview and personal opinion. If you find Vera's actions compelling, you may come to the conclusion that her practical joke is merely humorous. If, however, you find yourself sympathizing with Framton Nuttel, you may decide Vera's practical joke is cruel and inconsiderate.
In the story, Vera entertains herself at Framton Nuttel's expense. To Vera, Framton's naivety and hypochondriac tendencies are fair game to be exploited for her amusement. Framton is one of those individuals who labors "under the tolerably widespread delusion that total strangers and chance acquaintances are hungry for the least detail" of one's "ailments and infirmities." As a character, Framton may come across as presumptuous and sanctimonious. This may be one of the reasons Vera decides to play a practical joke on him.
At the same time, in her bid to be entertained, Vera appears to ignore Framton's feelings. She lacks empathy for her guest and is unrepentant about her actions. After Framton's hasty retreat, she concocts another tall tale to explain away Framton's apparently strange actions. She is not sorry for the grief she causes her aunt's guest.
In Framton's estimation, Vera's story is an unnerving one, and when he spies the men, he becomes totally horror-stricken. It never enters his mind that Vera might have made up the whole affair about the men's premature deaths. He is too frightened to think coherently about the whole matter, and this is why he feels compelled to leave immediately.

What does Montresor admit is his motive for this crime?

Montresor does not go into detail about what specifically motivates him to murder Fortunato but does mention that Fortunato had caused him a "thousand injuries" before insulting him one last time. Fortunato is depicted as an arrogant, proud man, who openly insults individuals like Luchresi without thinking twice.
Montresor is portrayed as a vengeful individual, who takes pride in his heritage and family's impressive name. While Montresor leads the unsuspecting Fortunato into the depths of his catacombs, he mentions that his descendants were "great" and "numerous." He also spends time elaborating on his family's coat of arms and motto, which means "No one provokes me with impunity"—this emphasizes his terrifying plan of revenge.
Given Fortunato's propensity for insulting individuals and Montresor's family pride, one can assume that Fortunato more than likely insulted Montresor's family name, which motivates him to murder Fortunato by burying him alive in the vaults of his palazzo.

Montresor says he has suffered a "thousand" injuries from Fortunato but that, in the end, it is an insult that leads him to plot revenge. However, although he feels his pride has been damaged, Montresor never reveals exactly what the final, unforgivable insult was that led him to believe he needed to protect his pride and family honor through murdering another person in a horrendous way.
We have to wonder if the actual injuries and insult have gradually become less important to Montresor as he stuffs down his anger—smiling and pretending everything is fine—and then consumes himself with plotting vengeance. The revenge seems to have taken on a mad life of its own. One wonders what Fortunato could possibly have done that was so terrible that he deserves the fate of a slow death walled up in a catacomb.

What is the climax of the story Number the Stars?

The climax of Lois Lowry's novel Number the Stars features the story's heroine, Annemarie, making the delivery of a package to her uncle. 
However, it might be helpful to provide a bit of background to explain the narrative that leads to the climax. The story opens in Copenhagen with the introduction of two girls, a pair of friends named Annemarie Johansen and Ellen Rosen. Nazis are slowly taking over Europe, which is a big problem for Ellen and her family in particular: they are Jewish, and they are afraid that they will be taken away to a concentration camp. 
Annemarie's family decides to help Ellen's family. Together, they hatch a plan: the Rosens will try to escape with their son, while Ellen will stay behind with the Johansens and pretend to be Lise, Annemarie's long-deceased older sister. When Nazis come to the Johansens' house, they are suspicious of Ellen's identity. As a result, the Johansens flee for Sweden, where they will stay with Uncle Henrik.
The plot gets pretty complicated here: what you need to know is that Henrik and Mr. Johansen stage a fake funeral for a nonexistent aunt. Annemarie does not understand why. But she later learns that Uncle Henrik is involved in smuggling Jewish people to safety. This leads us to the climax: Annemarie finds a packet of information that Mr. Rosen accidentally left behind. Something inside the packet, her mother realizes, is of tremendous value to the Resistance. Mrs. Johansen instructs Annemarie to take a basket, fill it with food, hide the packet inside it, and deliver it as fast as she can to her uncle Henrik.
Annemarie's journey to deliver the packet to Uncle Henrik is the climax of the book. She is intercepted by Nazis, who question her but ultimately let her go. It is an important moment because what she delivers to Uncle Henrik, as the rest of the book reveals, is critical to his mission to help Jewish people to safety.

What is the function of rhyme in "And Then There Were None"? Does it provide an underlying analogy about the nature of crime based on death as a result of intention or accident, or is it just a plot device to give structure to the murder mystery?

The nursery rhyme is mainly a plot device. The original rhyme "Ten Little Indians" concerns the unpleasant fate of a group of ten young Native Americans. At the start of the nursery rhyme, there are ten of them, but gradually, one by one, they come to a sticky end, until there's only one left— and he hangs himself.
Agatha Christie's use of the nursery rhyme foreshadows what happens in the story. Ten guests have been invited to a remote island, and in due course, each one ends up dead. Indeed, many of them end up suffering almost identical fates to the poor, unfortunate boys in the nursery rhyme. For example, in "Ten Little Indians" one of the boys manages to chop himself in half, leaving only six left. In "And Then There Were None" Thomas Rogers, the butler, is found dead after going outside to chop wood.