Yes, these are hints that she might like you. But that's it. I'm sure there are a lot of other people who like you and who behave on a similar way. Perhaps she just wants you two to be friends? And if so, what's wrong with that?
For what you've said, you two don't talk much, and are not particulary close. Perhaps you were afraid of rejection and built walls instead of bridges, and you weren't able to get closer to her as you wish.
I must say 2 months is too short time for one to get close enough to someone, but you could try. Talk to her, don't worry about what, just talk to her. If it is suppose to happen, then it'll happen no matter what. If, for some reason, you two don't get close and she moves away from you, well, that's how it was supposed to be, that's life goes. But don't worry, soon you'll meet many people on your life and you'll have plenty of oportunities to meet other people... You're still young, and life you'll teach you many things, you'll have disapointments and you'll have good moments...
I think the best advice I've heard about the subject was said by Thom Yorke (from Radiohead), and I quote:
"If you have been rejected many times in your life, then one more rejection then one more rejection isn't going to make much difference. If you're rejected, don't automatically assume it's your fault. The other person may have several reasons for not doing what you're asking her to do: none of it may have anything to do with you. Perhaps the person is busy or not feeling well or genuinely not interested in spending time with you. Rejections are part of everyday life. Don't let them bother you. Keep reaching out to others. Keep reaching out to others. When you begin to recieve positive responses, then you are on the right track. It's all a matter of numbers. Count the positive responses and forget about the rejections."