The best questions to ask are questions about their answers. That's how you get to know someone deeper, by asking for elaboration, tangents, association - the things that reflect how their minds actually work. A list of questions is going to sound like an extended pick up line.
I remember hearing (possibly reading) that there are 4 questions to ask a person to see I'd you're compatible.
1: do you like horror movies
2: would travel to a foreign country alone
3: if you could would you run away and start all over again
4: I can't remember number 4 but I'd suggest asking if they like pizza coz if they don't the other three questions don't even natter