What should I do - Long question?

It looks like she is kinda into you or she is just being nice. And the week you weren't on the train she must have thought you were avoiding here or something. If you want her to give you a chance just go up to her and say hi. It will be complicated moving around on a train to talk to her so ask her if she has a facebook, twitter, myspace, AIM, skype or any other type of socializing. GOOD LUCK:)