How to tell when a girl is interested in you?

It sounds like she's flirting with you, but at the same time, from my personal experience, I do that sort of thing to my guy friends a lot. I think that they know that I'm not flirting with them though. Her coat on the back of your chair is a good indication that she likes you and trusts you to watch her jacket for her. I'd say that you should ask her out for coffee or something. Get to know her. Maybe you can add her on facebook and get chatting with her that way first.