WHAT do I make of this girl? Is what I'm feeling normal? does this make any sense? Need a perspective on this?

From a 21 girl's perspective, I don't think she's serious about you. I think she is looking for someone who is "experienced" and someone she can have a good time with/ casually date (hence her on and off with other guy). You seem to want a serious relationship, and she doesn't understand that. I would say no in this situation. It seems like she wants a little bit of everything and control on the relationship if it progresses (wanting you to sleep in her bed even tho you're uncomfortable? Any consideration for what you want/ your comfort level?) Unless you can communicate your feelings for her, and express that you don't want the other guy in the picture, discuss boundary lines, then I would walk away. You can't make someone understand you, and if she can't respect your reasons for going slow, then she's not worth being around.