I guess that I can give the female point of view...
Don't believe everything people says online. Even when it is probable that she's telling the truth (it is only casual chat) and she knows that she will see you at school, that doesn't mean that all she says is true
She has a boyfriend and although if you're teenagers that doesn't mean much (relationships changes as the person matures... or doesn't mature :p) there's a principle that would help a lot if people (whatever age) could follow it through. You're in relationship? = Off limits. We can only be friends and that's it no matter how hard the temptation.
First, because there're would be the feelings of a third person involved, even if he's an a.... Don't do to others what you don't want for yourself
Second, because if it is true that she fancies you and, by accident, you kiss her or...whatever and her boyfriend learns about it, there's going to be trouble. That would be an unnecessary complication that nobody wants.
The fact that she contacted you doesn't have to mean a thing. Some people simply looooooves to have hundreds of people in their FB friend list (you can easy check that by looking the number of friends she has there).
The way you say it, it looks that she does fancy you but... is that really so? the thing is that we only have your point of view, and your point of view is that you want her to fancy you. So there's a risk there that you're not seeing reality, only what you would like it to be.
You say that you're good looking (beauty is in the eye of the beholder so maybe she doesn't consider you that attractive. Sorry if I burst your bubble) and that she's too. Maybe she is too inmature to appreciate true friendship and simply wants to be sourrounded by attractive people like herself.
Maybe she really likes you and she's taking the first steps to get closer to you. Being friends would be a good starting point but, anyway, until she breaks up for good with her boyfriend, going beyond friendship is a no-no.
Maybe she's just getting closer to you with the purpose of making her boyfriend jelous...
There are many details that we don't know and that I don't think that a person who wants things to be in a certain way can really measure or appreciate. And there are thousands of reasons why she contacted you that we can discuss. Most of the time, the simpler cause seems to be true. She was bored, searched for names that were familiar to her on FB, just out of curiosity, and that's why she found you because she didn't see you as a risk since she knew you were in the same school. No hidden purpose.
Still, you (and we) can go mad with the endless possibilities so, in summary:
In summary, I would keep the famous KISS principle (Keep It Simple Stupid)
- Don't try to figure out what she wants. You'll probably get it wrong. Whatever it has to be, it will be. And just figuring the whole thing out will give you headaches. It is not worth it.
PS: She's not your dream girl (not yet, at least). She may be beautiful but nobody is perfect. You simply don't know what's wrong with her yet. The only perfect person is the one that accepts you the way you are, that even if you fight with her still loves you, and stands by your side for better or worse. And then, it doesn't matter how she looks.
PS: what I really like in a boy is his intelligence and have curiosity, someone I can talk to about anything and well informed. I don't care if he's a geek or not. But if being a geek shows passion for whatever he likes, enthusiam and knowledge, so be it. I don't mind