She wants to have sex with you and all you can think about is studying.
Dude, if she wanted to have sex she'd be sending signals. Seriously, you know nothing about women.
Ok, from someone who actually has been pretty successful with women and am currently married happily let me give you some advice.
Firstly, she's interested. Not with sex per se, but with you. Touching (also laughing and slapping your arm, touching your knee for a second while talking to you, etc) is signs of comfortability. If she was not interested at all with you (friends or otherwise) she would not firstly, call it a "date" nor be at your house. She would choose a neutral place. She also would most assuredly not be the one to suggest your place.
Secondly, she finds you disarming and easy to talk to. She would not come over so late and mentioning staying up late if she found you to be a tool.
Now, what to do. I would start by sitting diagonal until such time that sitting next to her is acceptable. Such as reading something she is reading or she asks you to "come here and take a look at this", etc. I would also find out what she likes for a snack. if she likes salad whip up something cheap and easy "in case she gets hungry". Coffee wouldn't hurt either. I wouldn't assume anything. Get to know each other. Talk a bit. Take a break from studying for 20 mins or so (salad and coffee or sammiches, or whatever) and let her talk. Ask her stuff like how she chose the school, what she plans to do after graduating, etc. Keep it light and let her dictate the pace. Her comfortability is paramount.
I will say you have one thing going in your favor. She at least finds you interesting. Where it leads (if you want it to lead anywhere) is really up to HER.....not you