dude she's probably younger if she's living with her parents. I doubt very much that she's sexually secure enough to invite him over just to ****. Especially when her parents are around, but then again maybe she IS the type of girl to just want that.
I'm willing to bet she just wants to hang out and do something, with everything closed on good friday what else CAN u do? So in all seriousness man, don't make such a big deal of it.
Just don't worry too much about it, make jokes about the movie even or just make comments about her and how she is or something. Make small talk, ask what you're gonna watch, what the movie is about, if she's seen it before, what kind of movie it is... any one of those questions should do and just go from there. But above all, TRY TO WORK IN HUMOUR!! or else you appear boring or something else of that nature.
The big thing is, if you two are dating at this point and even if you're not. If you two are interested, I'd try to sit next to her and then slowly get closer. She'll give you hints if she wants you to leave her to herself. Some are vocal and will tell you to not touch her or sit so close, but most will just move away or will adjust themselves or something to give you the hint.
And if she rests her head on your shoulder or something, you should put your arm around her or stroke her hair or something like that. At least, these are thigns I do and so far no objections yet. But I'm not sure if they do anything for these women or not.
btw, i just read the message you left in another guys post about dating. you told him how to handle himself on the first and second date and you're asking advice about it? You're probably fine and are just thinking too much about it then, you probably have it within you.
Good luck