What questions can get a conversation going?

I like this one girl in one of my university classes we've Bennett friends for a few months but we're more 'classroom friends' rather than actual friends, so I want to get to know her better. I don't see her much in the week only when I go to class so I message her on FB when I really miss her. So far we only message each other when it comes to homework and I don't want her to think I only want to talk to her about class subjects. So what questions can I ask?

(It's a little weird, I remember one time I straight up told her I want to get to know her better and she never replied but when I ask questions about her in a Suttle way she becomes talkative, why is that)