The first step would be to identify the theme. A theme is a life-truth that the author is trying to share with his/her audience. For this story, the theme could be "familiarity breeds contempt," "justice will prevail," or "you cannot hide the evil within." There are certainly others, based on how the story speaks to each reader, but I find these to be prevalent.
If we choose the last theme, "you cannot hide the evil within," you can apply all the literary elements you have identified.
The plot is about a man who changes from being loving to animals and people, to being one consumed by hatred for both.
This, too, covers the character of the man. He has been loving of animals for his entire life; he meets and marries a woman with similar feelings. As time goes by, he loses touch with this aspect of himself, loses all patience and compassion, and resorts to torture, and ultimately, committing murder.
Point of view is important with this theme because it is only by being able to look into the very mind and soul of our narrator (from a first person point of view) that we can not only witness his degradation as a person (drunkenness, abuse, etc.), but we can also watch (and listen to) how his obvious psychosis permeates his entire being and destroys the kindness and gentleness that once resided within.
In terms of the setting, a great deal of the dark side of the story occurs in "dark" places. The establishments he haunts each evening are vile. It is there that he becomes repeatedly drunk, and it is there that his soul begins its deterioration. The other specific setting of the story is the basement of his home: a dark, chilling stage on which the narrator plays out his final, maniacal act of hatred, and his attempt to cover his actions.
An author's style is the way he/she writes, how he expresses himself, grammatical structure, and even the specific words he chooses to create his own particular way of writing.
Poe's style is very specific to his writing. It lends itself to creating horror stories. Those who remember Alfred Hitchcock will note that his stories, on TV or in the movies, always created a sense of horror. A more contemporary parallel would be Stephen King, though his style diverges greatly between stories such as Carrie, and others like The Shawshank Redemption or The Green Mile. In all of these cases, the stories are told in such a way as to elicit a contrived response: we are to be horrified, even fascinated, and certainly drawn in by the writing style.
When studying The Black Cat, the words Poe chooses to create a sense of suspense, shock and even revulsion stand out: dread, felon, terror, horror, gallows and perverseness (both in capital letters), rabid, and death are words that set a specific mood and purpose for the reader: to bring about horror and fear. With these words, the theme is clear: you cannot hide the evil that lies within. With the end of the story, the cat (the one in the title? who knows?) does, in fact, reveal the evil hidden within the man.