Okay, hands up, girls.

1) How many of you would lower your opinion of a guy you like if he asked you what you want to do?
2) How many of you would lower your opinion of a guy if he thought it would be a terrible thing to ask you what you want to do?

Seriously, Peeg, if you're judging her intelligence as smart and you're saying that you're more grown up than her just because you're older than she is, then I have something to say to you: If she's smart, she won't think anything bad of you for asking such a question - because there's nothing bad about it, and only a stupid person would think badly of a person for such a stupid readson. Also, you still have growing up to do yourself if you think that asking such a simple question is going to cause such dramatic problems.

If she likes you, she'll like that you are showing an interest in her.
If she doesn't like you, she won't like that you are showing an interest in her.

You don't even have to do these things. If you're still that silly about it all then I would suggest you simply get her onto Facebook and then check out her interests - which, oddly enough, you seem to know a fair bit about already so I don't really know what the big deal is. You've listed a bunch of things she likes. She'll do things she likes, right?

EDIT: Also, if she says "Whatever you want to do" then do whatever you want to do. Sometimes it's a good thing to show who you are, and if she doesn't like it then it wasn't going to work out anyway, was it? If she likes it, hooray, you're doing great.