My fiance is going to have her appt with the US embassy this friday. What kind of question do they ask?

Answer 1

They will want proof that the relationship is legitimate, things such as, letters & e-mails that they can see the postmark or dates on, pics of the 2 of you together...etc. They might ask questions about any relatives to see if you both know about each others' families.
Also, they might ask questions to see if you both answer the same. For instance when I talked to the embassy about my husband to make his appointment, they asked his phone numbers.(I was in his country.) I gave them the home & cell number. Then they asked me, "What neighborhood do you live in?" I answered, and he asked, "Oh is that near so & so?(he named a nearby town) I answered that we were about 15 minutes south of that town, so he said, "Oh I can tell you live there because you knew the numbers pretty good and from your description you know this area."
That's the main things I can think of.

Answer 2

We usually ask when you met and how, how often you saw each other or dated, when you decided to get married. We also sometimes ask questions about the other person's family - things like names, relationships, pets, what they do for work or where they study - normal things that a real fiance would know. We are looking for a real, normal (for that culture) relationship that will logically lead to marriage.