In “How to Date a Browngirl, Blackgirl, Whitegirl, or Halfie,” by Junot Diaz, what are some of the differences in the narrator's expectations these different categories of women? How do the different expectations cause the narrator to treat them differently on the date?

These two questions are not easily answered.  The reason for that is because the narrator switches descriptions of the girls so quickly and so often that it is difficult to keep track of which ethnicity and socio-economic background any particular girl belongs to.  As the background of the girl changes, so do the narrator's actions, and the text becomes more confusing because the narrator sometimes changes his actions without telling readers that the girl has changed.  
What is very clear, though, is that the narrator absolutely believes that he must do two things in order to impress a girl and perhaps get some physical intimacy with her. First, the narrator believes that he must hide his own ethnicity.  That's why he feels that he has to hide pictures of his "family in the campo."  It's also why he doesn't ask the "halfie" how she feels about Dominicans.  

You'll wonder how she feels about Dominicans. Don't ask.

Second, the narrator feels that he has to hide as much of his socio-economic status as possible.  He's from a poor family, and he wants to hide as much of that as he can.  That's why the narrator hides the cheese in the beginning of the story.  He doesn't want the girl to know that his family is on welfare. 

Clear the government cheese from the refrigerator.

Just as the narrator wants to hide his ethnicity and financial status, he narrates how knowing those two things about a particular girl can help him in his conquest of her.  The narrator tells readers on two different occasions how skin color helps him determine how far he can go on a date with a girl.  

A local girl may have hips and a thick ass but she won't be quick about letting you touch. . . She might just chill with you and then go home. She might kiss you and then go, or she might, if she's reckless, give it up, but that's rare. Kissing will suffice. A white girl might just give it up right then. 

In general, it seems that the lighter the girl's skin color is, the more confident he feels about his success with the girl.  
While the ethnicity and skin color play into his wooing strategies, the girl's socio-economic background appears to be equally important to the narrator.  That's why he makes a point of explaining why different restaurants are needed for girls that either are or are not from "around the way."  That part of the girl's background also guides which direction the narrator takes the conversation.  

As you walk to the restaurant talk about school. A local girl won't need stories about the neighborhood but the other ones might.