To answer the "How much of a relationship is in your head?" question, until you see some form of reciprocation you won't know for sure. Even if she says she doesn't want to date you, you still won't know why and she probably won't know why either. People can have extreme difficulty expressing and even understanding their own feelings and why they feel them.
This. Girls are crazy (and so are men, actually). I remember when I started trying to hang out/date my current girlfriend and it was hard as hell. I had been with her many times, accompanied by a mutual friend who had set us up, and we got along really well. still, whenever I tried to arrange something, just me and her, she'd make up some excuse. Eventually I made it, through a lot of patience and romantic endeavours. Nowadays, when I ask her why she made up excuses back in the day, she says she doesn't know. She was probably afraid of god knows what, as she is afraid of a lot of things, as all of us are, most times because of a whole lot of reasons we're not aware of.
So good luck, ahah. Anyway my advice is ask her again a few days from now and see how it goes. don't give up but don't push it aswell.