In talking about their upcoming date, Blanche actually speaks only about herself. She talks about the ways she has misrepresented her age and sexual experience: "he thinks I’m sort of—prim and proper." She does not speak about any of his attributes that she appreciates. Rather, he is a vehicle for her to escape Stella and Stanley’s apartment: "If it happens, I can leave here and not be anyone’s problem."

Mitch, clearly, is not a person to her; he occupies the position of yet another shining knight. She therefore distorts her own image by lying to him, as well as to herself, in her attempt to fit the picture of the two of them together. When he uncovers the numerous fibs she has told him, she counters with her own logic, saying, "I never lied in my heart." Even at this late stage, she cannot and will not admit responsibility for her actions.

Blanche wants Mitch because he represents her last hope for a husband and someone to support her. She has lost her girlhood home, has no marketable skills, is becoming more and more mentally unbalanced. She had been a schoolteacher but was dismissed for having a relationship with a student. She also has sexual desires that she tries to subdue but sometimes get her into trouble. She does not want to have to live with her sister for the rest of her life because she and Stanley do not get along. As unrealistic as it may be, Mitch represents escape from all of her problems. She would have her own home and someone to support her if she could impress Mitch enough to get him to marry her.

Blanche explicitly says that she does indeed want Mitch. With his courtliness, immaculate dress sense, and his old-fashioned Southern manners, he's a breath of fresh air. Certainly, he's a welcome change from most of the men she comes across, the "apes" as she calls them—particularly Stanley:

“I want to rest! I want to breathe quietly again! Yes—I want Mitch…very badly!”

Blanche desperately needs to be loved, needs to be protected from a harsh, unforgiving world which has treated her so badly. And Mitch appears just the man for the job. Blanche also comes to look upon Mitch as some kind of savior figure, someone who can save her from a disreputable past. But this is pure fantasy on Blanche's part.

In fact, Mitch's desire for Blanche is also a fantasy. He perceives her to be a fine, upstanding, respectable Southern belle. However, when he finds out the true nature of her sordid past, the scales fall from his eyes immediately. She's not the woman he thought she was; she's the complete antithesis of the ideal fantasy figure he's constructed to fill a gaping emotional void. And when Mitch finds out about the real Blanche, she gets to see the real Mitch—a violent, would-be rapist who's just like every man she's ever met.

Ultimately, they both realize that it's not what they want, but what society will allow, that really matters in such a time and such a place.

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.

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.

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.

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 title of the play comes from the streetcar that Blanche takes to get to Stella and Stanley's flat:

BLANCHE: They told me to take a streetcar named Desire, and then transfer to one called Cemeteries and ride six blocks and get off at—Elysian Fields!

However, the title means more than just a physical landmark. Blanche mentions the streetcar again in scene four, the morning after the poker game. Blanche can't understand why Stella would return to Stanley after the way he behaves, and Stella responds:

STELLA: But there are things that happen between a man and a woman in the dark—that sort of make everything else seem—unimportant

[Pause.]

BLANCHE: What you are talking about is brutal desire—just—Desire!—the name of that rattle-trap streetcar that bangs through the Quarter, up one old narrow street and down another...

STELLA: Haven't you ever ridden on that streetcar?

BLANCHE: It brought me here.

Blanche establishes the streetcar as a metaphor for what it is named after—desire. We should also note that Elysian Fields, where the Kowalskis live, is the land of the dead in Greek mythology. Thus, Blanche's sexual desires lead to her downfall.

The streetcar is mentioned again in scene six, after Blanche's date with Mitch:

MITCH: I guess it must be pretty late—and you're tired.

BLANCHE: Even the hot tamale man has deserted the street, and he hangs on till the end. [Mitch laughs uneasily again] How will you get home?

MITCH: I'll walk over to Bourbon and catch an owl-car.

BLANCHE [laughing grimly]: Is that streetcar named Desire still grinding along the tracks at this hour?

MITCH [heavily]: I'm afraid you haven't gotten much fun out of this evening, Blanche.

On the surface, this appears to be small talk amidst their uneasy laughter as an attempt to end the awkwardness of the evening. But given what we've already established, we know the streetcar has a deeper meaning. There are sexual undertones to this question. Perhaps it is a reflection of Blanche's desire of Mitch. Perhaps it is a way for Blanche to get Mitch to think about his own desires. Blanche wants Mitch to pursue her, but she can't outwardly say that or come on too strong. She must act like a classy, proper lady and can barely allow him to kiss her.

Stanley dislikes Blanche for a variety of reasons. He calls out her lying and snobbish attitude repeatedly. However, the one thing he appears to resent most about her presence in the house is its effect on his married life with Stella.

Stanley describes his married life as having been ideal before Blanche's appearance. Stella's attraction to him comes from his raw and unashamed masculine sensuality, which serves as a startling contrast to the more restrained and genteel world she and Blanche come from at Belle Reve. It also appears that Stella was never ashamed of Stanley's working class ways before Blanche came or that she ever challenged Stanley's authority in any significant manner. Blanche's presence reminds Stella of a more refined way of life that Stanley cannot stand. When Stella starts criticizing Stanley's manners, he loses his temper and behaves violently, viewing himself as a "king" over his own domicile. In this sense, Blanche is trying to overthrow Stanley from what he perceives to be his rightful place.

Ultimately, this desire to keep his household authority is what makes Stanley despise Blanche and causes him to rape her during their climactic confrontation.