OK, so there is this girl in my class who I think is flirting with me. I kind of like her. She will walk half way across the class and find a reason to talk to me. She will ask me for, or loan me, a pen. She'll also talk to me in the halls. Should I flirt back or ask her to a movie and see what happens?

Yes. Why not? You say you like her so go for it!

Didn't you already ask this question?