In the twentieth and twenty-first century, "Reality and its truth had gone inward." What does it mean when it says "Reality and its truth had gone inward"?

I assume this question is asking about how the quote applies to the literature of the twentieth and twenty-first centuries. The quote, "Reality and its truth had gone inward," suggests, to me, that the writer is claiming that literature of this time focuses more on the inner workings of the protagonists' minds. This style of literature is most often associated with "Modernism" and "Post-Modernism" and, in terms of time period, coincides with the rise of psychology as a discipline.
If you think about psychology and what it studies and then relate that to literature, you can see the meaning of the quote more clearly. Psychology studies how the human brain functions, how it develops through different stages, what happens when a brain functions abnormally, and so on. Literature has always been about telling stories about people, about characters. From the Modernist era on, some authors' new interest in psychology meant that they would try to replicate the workings of the human mind more accurately in their novels. This is where the style "stream-of-consciousness" comes in: this is a form of writing in which the author writes from inside the character's mind trying to show how a mind actually works. Rather than organizing and structuring thoughts in ways that are easier for readers to follow, the authors may show characters making free associations from one train of thought to another, without warning. This means the prose can also be more difficult for a reader to follow.
During the period of Modernism and after, most of the authors of this time period lived through World Wars I and/or II or lived in a world after those global conflicts. Those events also changed how people related to the world around them. They could no longer trust religion or government to necessarily protect them. It's easy to see how people could retreat inward and feel more psychologically fractured. This is a mental state many authors tried to capture in their prose—or perhaps, it just reflected how people had come to think in this era.
Some of the authors whose work most lines up with the sentiment in the quote are William Faulkner (especially in The Sound and the Fury and As I Lay Dying) and Virginia Woolf (Mrs. Dalloway, The Waves). James Joyce's Ulysses and Finnegan's Wake are even more extreme examples. Again, to recap, "reality and its truth had gone inward" suggests that authors now sought to only record "truth" or "real life" insofar as it was seen from the perspective of the individual.

What impact did the Pilgrims going to America have?

The impact of the Pilgrims on America is likely not as substantial as most America History textbooks make it. The pilgrims were not the first settlers from Britain in North America. Virginia was granted a royal charter in 1606 to found a colony, though English settlers had resided in Virginia since about 1590. The initial settlement of Roanoke was abandoned by 1590, but the Jamestown settlement was ultimately a success. Jamestown faced several rough years, due largely to placing an inordinate amount of resources into searching for exportable commodities and placing too little effort on growing food. After learning to grow tobacco (as well as the necessary food) the settlement began to flourish. Tobacco became the cash crop of Virginia and, in order to maximize profits for the crown, led to the importation of African slaves because Native American slaves were unsuitable for the task. The first African slaves arrived before the Pilgrims landed on Plymouth rock.
What would later become the New York colony was initially settled by the Dutch before the Pilgrims landed on Plymouth rock as well. The Pilgrims, therefore, were not the initiators of colonization nor did they drive colonization north of Virginia. However, the Pilgrims did have two impacts on how the New England colonies developed. First, the Puritans demonstrated a religious intolerance that is surprising considering the reason for settling in North America was religious intolerance against Puritans in England. This religious intolerance ultimately led to the founding of Delaware by dissenters. The religious intolerance was also connected to the importance of religion in the legal and governing aspects of the Massachusetts Bay colony. This helped prolong the impacts of the Salem Witch trials (as well as nearby witch hunts), though it was not the leading cause.
The second impact was the governing style of New England. Because the Pilgrims landed outside of land that belonged to the English Crown and established a self-governing settlement under the Mayflower Compact prior to obtaining a royal charter, settlers in the Massachusetts Bay Colony retained a substantial amount of involvement in the political processes compared to other colonies.
These issues likely had little long term or significant impact on the development of America, though they do provide useful historical studies.

Can Sir Arthur Conan Doyle's The Sign of Four be classed as a hybrid work that mixes genres and writing styles? Why?

Sir Arthur Conan Doyle's The Sign of Four is a detective novel. This is a genre which evolved in English literature out of certain elements of the sensation novel. While The Moonstone (1868) by Wilkie Collins is often considered the first proper detective novel, many other works by sensation novelists like Collins and Mary Elizabeth Braddon start with some sort of mysterious crime and follow a narrative trajectory in which the main plotline involves discovery of the identity of the criminal. Looking further back in history, some have even argued that Sophocles's Oedipus Rex was the first detective story.
In terms of genre, the mystery or detective novel is usually considered to be plot- rather than character-driven. It has fast-paced action, with a mysterious act or crime that occurred before or at the start of the novel being solved by the end of the work. There is usually a complex plot with many twists, red herrings, and clues that only fully make sense to the reader when all is revealed in the final chapters. Characters tend to be painted in fairly broad strokes, often having strikingly distinctive characteristics but lacking complex psychological portraits. Doyle's novel is thus typical of the genre as it evolved in the Victorian era.

Arthur Conan Doyle’s works featuring the brilliant Sherlock Holmes are regarded today as some of the greatest detective fiction ever written. It must be kept in mind, however, that before Conan Doyle, “detective fiction” was not a specific genre. Edgar Allan Poe had made significant progress in popularizing this type of story with his detective Auguste Dupin some sixty years before Sherlock Holmes emerged, and Conan Doyle was far from shy about his admiration for Poe. Conan Doyle did not only write Sherlock Holmes books, however. Decades before, he had begun writing Gothic tales.
In regard to The Sign of Four, therefore, it is appropriate to consider it both a detective story and a Gothic tale. The central case that occupies Holmes—solving the mystery that Mary has brought to him—puts it squarely within the detective fiction genre. Elements that link it to Gothic romance include the character of Mary, an innocent damsel in need of aid; the mysterious settings of London’s dark streets, especially the gloomy, castle-like Pondicherry Lodge; the search for lost treasure; and the exotic, Orientalist elements of the Indian islands.
https://books.google.com/books?id=i9ZjDwAAQBAJ&source=gbs_navlinks_s

Which popular filmmaking movement believed in basing a film on one person's vision?

The idea of the auteur, French for author or originator, is at the center of cinematic approaches that emphasize the vision of one person, generally the director. Auteur theory guided the French New Wave movement of the late 1940s to 1960s. Important articles promoting this point of view appeared in the journal Cahiers du Cinema. From the original film concept to the writing and supervision of the script, the direction of cinematography, the casting, and the choice of score—all should be subject to the director’s control. Although the theorists who argued for the singular, guiding vision of the director were promoting this ideal in French cinema, they cited influential precursors in England and the United States, notably Charles Chaplin and Orson Welles. Important French directors in this movement are François Truffaut and Jean-Luc Godard.
https://www.britannica.com/art/auteur-theory

Was Reconstruction more of a success, or more of a failure? Please use at least three examples to justify and explain your decision.

This question looks for your opinion on a very complicated period in American history. In my opinion, I think Reconstruction was more of a failure. Southern states passed laws to limit African American suffrage, such as literacy tests and poll taxes. After the end of military Reconstruction, African American voter turnout dropped sharply. Poor whites could vote provided that they voted for Democrats. The Freedman's Bureau, while a good idea on paper, was not funded very well; the South remained poor for decades after the war. Sharecropping replaced slavery as the new way to keep the underclass down and it led to generational poverty for whites and blacks alike. Finally, the South lagged behind the rest of the nation in terms of education, investment, and wealth for years after the war. While Henry Grady spoke highly of the New South with its industrial opportunities, the South still did not receive a great deal of outside investment for rail production compared to the Western states. The South was eventually able to fund public education through property taxes, but without government incentives, this too lagged behind the rest of the nation. After the war, the federal government wanted to remain in the South for as little as possible. It would have been outside the norm at the time for government to become involved in private investment. Many areas of the South would remain poor until WWII when people left to fight or to work in defense industries. It took most of the region eighty years to get back on its feet--additional government capital and incentives may have helped.

In his famous soliloquy "To be or not to be," what does Hamlet contemplate?

In this well-known soliloquy, which is probably the most famous speech in the English language, Hamlet contemplates the question of death in the abstract. The line that everyone remembers—"To be, or not to be, that is the question"—implies very strongly that this question is for humanity as a whole. The possible answers to death, however, can only be provided by individuals themselves, taking into account their own unique circumstances.
Everyone is engaged in a perpetual struggle for existence and must ask themselves whether or not it is worthwhile, whether or not they should continue to "take arms against a sea of troubles." Ultimately, our choice in the matter is determined by what is "nobler in the mind." Once again, Hamlet highlights the wholly subjective nature of suicide, a choice that only we can make for ourselves. In making that decision, we will tend to do what is right by us rather than blindly following the dictates of some universal ethical system. Death may be an abstract question, but the manner of its determination, its answer to the question, if you will, is always concrete and particular.

Hamlet is contemplating suicide and death itself. To exist or not to exist is the question he debates aloud to himself.
This is not the only time Hamlet considers death, and this theme permeates the play. He is depressed over Claudius's murder of his father, an act he learns of from the ghost of his father. He talks to Yorick, the skull of a court jester he was fond of. In the speech, he compares death to a permanent sleep, which he thinks would be fine. However, he fears the possibility of it being a terrible never-ending dream.
Hamlet mulls over whether enduring the bad parts of life is better than risking the unknown territory of death. Hamlet chooses not kill himself, and the soliloquy is an example of his tendency to be indecisive.

How does Tim O'Brien respond to the conflict in "On the Rainy River"?

“On the Rainy River” details how O’Brien, newly graduated from college, nearly flees to Canada rather than go off to war in Vietnam after receiving a draft notice. The central conflict of this chapter is within O’Brien’s mind, since he is torn between going to Vietnam or dodging the draft.
O’Brien’s hometown community exerts unnamed pressure on the young man to make his town proud and bravely travel to Vietnam and emerge a hero. However, O’Brien protested the war during his time at university, and he believes the Vietnam War is murky and morally ambiguous.
O’Brien knows that fleeing to Canada will cause everyone at home to ridicule or criticize him, maybe even his own parents. He also knows that going to Vietnam is in direct opposition to his deeply held core belief that the war is not a just one.
Ultimately, O’Brien is faced with the dilemma of making a decision: go on to Canada on the other side of the Rainy River, or go back toward Minnesota—and thereby, the war. After crying and trying to convince himself to have the courage to cross into Canada, O’Brien decides to say nothing to Elroy, causing him to drive the boat back toward the US shore. O’Brien makes his decision using inaction, which perfectly captures his conflicted feelings about both options.
O’Brien fulfills his obligation to go to Vietnam out of deep-seated feelings of shame. Shame for not having more courage to stand up for his beliefs, and shame for running off so suddenly and disappearing.