What does Stanley want from/for Blanche and why?
When it comes to what Stanley wants from Blanche (in Tennessee Williams' play A Streetcar Named Desire) many different thoughts could be justifiable. One could easily justify any of the suggestions which were made in the posting. Does Stanley wish to break Blanche? Does he wish to see her fail? I would suggest a "yes" to both.
Stanley does not seem to like Blanche from the very beginning. After he finds out about her possible wealth (from the assumed sale of Belle Reve), Stanley begins to push Blanche. Once the truth comes out, that there is no money, Stanley beings to distrust Blanche and look into her past. He brings up Blanche's past to Stella in order to jade her views regarding her sister.
It seems that Stanley wishes Blanche to leave his home because of the conflict which arises between Stella and himself. Stanley wants his laid back life back and, with Blanche being there, he cannot achieve this.
As for wanting to sleep with her or not, I think that desire is not the real issue. Stanley knows about Blanche's past and her prostitution. He also knows that she is slowly losing her mind. In the end, the rape of Blanche is what forces Stella to commit Blanche. One could easily justify that Stanley raped Blanche only to force her out of his home.
The dynamic of "A Streetcar Named Desire" is actually very simple. Two people are fighting over control of a third. In this case it is Stanley and Blanche who are fighting over Stella. Blanche is the protagonist. She is the one who is disrupting the status quo. Though Stanley seems big and strong, he is on the defensive. He is the antagonist. He would have done nothing to or about Blanche if she hadn't moved into his home and started turning Stella against him. Stella is the "bone of contention" in this conflict, otherwise known as the MacGuffin. Although Blanche seems sweet and dainty, she is a dangerous opponent. The protagonist and antagonist are evenly matched. Lajos Egri discusses these matters in his excellent book The Art of Dramatic Writing, including the need for one character who is strongly motivated (in this case Blanche, who is fighting for her existence) and the need for protagonist and antagonist to be evenly matched. Blanche is an intruder, a nuisance, an unwelcome guest. Stanley just wants to get rid of her, and he doesn't much care how he does it.
More than anything else, Stanley Kowalski abhors pretense. He suspects Blanche's deception from the beginning and intensely dislikes her use of deceit to manipulate others. Stanley unmasks all Blanche's pretensions. His rape of her is his brutal response to her flirtations; if she feigns to have sexual desires about him, he will strike through her deception. In Stanley, she does not threaten his masculinity at all. Blanch is a nuisance and she exerts some influence over Stella, so he wishes to be rid of her.
I think we need to be aware of the way in which Stanley seeks to impose his masculinity upon Blanche throughout the play. Blanche is a character who threatens his masculinity in a number of ways, and of course her relationship with Stella is something that deeply troubles Stanley. What Stanley wants therefore is to impose his power on Blanche. I agree with #2 that the rape is not about desire so much as it is about power.
One thing Stanley want is total dominance over Blanch that lacks any semblance of personal relationship: he wants power that is devoid of moral undertones; he wants animalistic power that has no recognition of danger or fear. This is because his character is drawn as one who is animalistic and devoid of higher human traits and values.