When formatting an essay, does the topic sentence of the new paragraph always need to correlate with the last sentence of the latter paragraph?

No. When starting a new paragraph, an indent implies that a new idea is being presented. In the best essays, there is no expectation for the new paragraph to mirror the last. However, in the top essays, each sentence in the paper's entirety should like falling dominoes. No sentence should pop off the page, but rather should gradually be revealing itself. In writing, the most important thing to remember is the reader does not know what you are thinking, therefore your ideas need to smoothly be laid out.

How many hours is a day a fair amount of time to give to studying?

The best way to study is to not set up one specific block of time, but rather graze throughout the day. When setting up a projected hour to hour bases of studying, it creates pressure which cultivates into anxiety, which takes away from retention. The best way to study is to carry around flashcards or notes and study 10-15 minutes here and there, for the totality of the day. That way the information is not being force fed to you, but rather becoming a part of your daily life. This way you actually learn the information, and not just memorize.

How does the Point of View in "Hamlet" affect the overall meaning of the piece?

The story is written in Objective Third Person, which creates that dramatic effect of the play. It is not omniscient, whereas the reader we can get inside of the characters minds. All we have is their asides and soliloquies to depict what they are thinking. Since the reader has to use only direct evidence to distinguish motive and turmoil, this creates a more reliable plot.