Does this girl like me or is she just being very friendly towards me?

It sounds like this girl definitely likes you. When a girl breaks the the touch barrier, wants to spend lunch with you, and especially when she teases you about things like buying her gifts, those are HUGE signs that she likes you. I'd say let it progress for a couple more weeks and be just as flirty back to her. If by then she still seems to be doing the same things, I'd say take the next step and ask her to go to a movie with you or dinner some night. DO NOT just let it go because you don't want to be regretting it later in life trying to figure out if she really liked you or not. Who knows, maybe she's the one for you. :) Be sweet to her, take it slow and good luck! :D