Yup. Agreed. She is seriously weird. I would be careful around her not let things move too fast. I don't think she is aware of how you feel about her (even if she does, she seems to take things a bit too lightly) and since you have feelings for her, better slow things down and think through it more carefully instead of acting out due to your feelings.

I think being careful not to get your heart stomped on is the only advice I can give, and stay smart, try to be friends first and get to know each other, see where it leads.