Questions

no.1: Raskolnikov kills the pawnbroker because he hates her, of course that the fact that he owes her money makes it more complicated but his hate toeards her is what makes him swing that axe. Most of the people would confess that they hate or have hated someone, but kill them in response probably was never in their minds, that makes Raskolnikov especial, not because he is diferent that other people, but because he wants to prove to himself that nobody can treat him like a dog, for him she should be as miserable as him.

no.2:As we know Raskolnikov is never mentally balanced throughout the book, there´s always something bothering him, even before the murder of the pawnbroker, he clearly had a lot of evidence of missing sanity, one example could be the fact that by just meeting the woman he wants to kill her, or his constant disorder in his room, or even the fact that he goes to the bar, i can relate by experience that if a man drinks, it isn´t because he has a happy life, alcohol compensates the lack of euforia, or if you want to call it "happiness".

no.4:I personaly wrote about Razumihin in my essay, and i must admit, i kind of reflect a little of myself in his alternate series of events, as i view it, Razumihin helps Raskolnikov not because he is his dear friend, but because he compensate the evliness within him, his own darkness. Raskolnikov does seem better of a person thanks to Razumihin, and we could see this by acts like when he tells Raskolnikov about his mother money, and makes his pride go a little away, or how Raskolnikov finds sort of good that Razumihin likes the housekeeper, we could even say that when he helps him recover while sleeping, gives us a view that Raskolnikov enough good to have friends that worry for him.