Need Advice Quick!!!!

[Sdfarmer]

So a little background first, its the first few weeks of college and i am a freshman. I've never had a girlfriend so everything past that has also never happened. The first day of classes i meet this girl who seems honestly just as lost as me going to lectures, after talking to her a bit we both have chem together and i decide that might be a great way to meet new people and more importantly maybe find a girlfriend. I end up getting her Snapchat and 3 weeks later we've been to 2 study sessions (i never said anything about dates) and we've gone to the library each time and only studied. Granted there were jokes and little flirty comments exchanged but nothing too obvious. Now she on the third study session she asks if we go to this food court in the mall on campus instead of the library or anywhere else and of course i agree and we end up finishing the homework in like 20 minutes and i suggest that we get something like ice cream to eat after. We eat our ice cream while walking around the city just talking it up and then after about an hour she asks if I would like to see her house (shes renting a room in a house off campus while i am in a dorm) so I say heck yes why not. So we go to her house, she gives me a tour, and brings me into her room and i take a seat on her bed and she sits in the chair right next to the bed. We talk for like 10 or 15 min and she doesn't really move from the chair and mentions that she has soccer practice in like an hour but that we still have time to hang before she has to go. We end up in the living room somehow and keep talking until she has to start getting ready for soccer and then drives me back to where we met up for studying. On the way back she tells me that if i end up getting an apartment next year that she would be down to be my roommate, i respond very positively to her suggestion and we part ways after her dropping me off. Now end of backstory, sorry it's so long just didn't want to leave out any details that i might not think are important. I'm left with a couple questions from the time we spent with each other first: Is she into me romantically? i get conflicting things like she invites me over to her house and i'm sitting on her bed and everything but she doesn't make a move (part of the second question too) and she asked if i wanted to room with her which makes me think she might not know i'm straight and that would be really embarrassing. Second: was i supposed to make a move when we were in her room and if so what should i have done. I am not looking for just sex, wouldn't mind it but i really think shes a cool girl and very pretty that I would want to be with and i just want some fresh eyes on the situation besides my own.

[ThatwasThen]

I think she is interested in getting to know you better and that she purposely sat in the chair and not on the bed because she didn't want to give you the idea that she was up for sex with you yet. I think that you should go in for a kiss next time you are together and she appears to be wanting you to kiss her. "Tells" that she is interested in you as more then just friends are: Her leaning in close to you, being touchy feely, flirting etc. You don't want to rush things but you don't want to put yourself so far into the friend zone that she doesn't feel you romantically either.

[Sdfarmer]

I was thinking the next time we see each other, which would be in a lecture since we sit next to each other most of the time, if she would like to go on a date sometime (emphasis on the date part). Or should i just keep doing the study sessions with her? I just want her to know that I like her so that way i don't end up in the friend zone. And what are some good tells i can give?