Thats a really high compliment meaning that you're really good looking.Honestly I can't say she is lying nor is she telling the truth because I'm not actually there or can tell if she is or not.Most liekly she wouldn't be lying though :) your next best move is to give her a nice compliment or better yet a kiss ^_^
Handsome is more classy like beautiful, or has more sincerity.
she is... interested! DUH ;D
She means that you're handsome. That's all. I HATE it when guys take a compliment as an invitation to hit on me. Don't think too much into it please.
Well the next move would be a thank-you. She probably thinks you're handsome. Doesn't necessarily mean anything, just that you look. Don't take a simple compliment for anything more than that. It could be a compliment or an invitation. Depends on the girl. Why don't you ask her and find out?