Oh the possible scenarios…
1) She knows you like her and enjoys your attention, but has no intentions of taking it further but she gives you enough ‘signs’ to keep you hoping, so that she won’t lose your attention. If that is the case, you should leave well enough alone, you can keep the friendship but make opportunities for other girls to enter your life (if you want).
2) She is a touchy feely person, thinks of you as a good friend and really has no idea that she is giving you mixed signals. She figures she is turning you down when you ask her out, so you should know she doesn’t want to be more than friends. If this is the case, then you should talk to her honestly and let her know that you are getting mixed signals. If you guys are really friends, then be honest about this should only strengthen your friendship.
3) Some other scenario that I haven’t thought of yet…..
As for impressing her….I wouldn’t try, I’d just be yourself (I know it’s cliche). However, (and I’m speaking from experience) sometimes when a girl (or guy) is friends with a guy (or girl) and that guy (or girl) is always right there the girl (or guy) doesn’t realize what a terrific guy (or girl) she (or he) has right in front of her (him) until there is some distance between them and they have the chance to start missing the guy (or girl). I’m not talking about a hostile distance, just maybe have some other things going on that don’t involve her, give her a chance to miss having you around.