The situation is like this; I like her, but cannot get her at the moment. She is a good friend with my friend (if you know what I mean). I wouldn't touch my friend's women. Altough we're not really close friends and they do not really date... but anyway.

But I've liked here even since I saw her. Lately we got to know each other and we get along well. She gives some IOIs, we laugh a lot, she clicks me on FB a lot, etc.

I would like to get/keep her attracted to me and not slip into the friend zone. Right now, we talk a lot on FB and we see each other in school. (she always smiles when she sees me ) I'm just afraid that by the time she will be "free" for me, I'll be "just a friend".

So I guess I should use some push-pull? Not talk to her for a while, be cold, and then be the nice person again?

And, it is ok if we talk about serious subjetcs, like personal problems (for example, divroced parents) ? Is it good if she trusts me her problems and I her, or will that put me in the stupid friend zone?

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Stay cool.

about your moral problem;
Just ask your Bro what his plans are with her and then add a single word that will convince him to leave her for you. The word is; DIBS!

about what to do about getting her. Talking about personal stuff is okay if you want to have a relationship with her, but do it personally not over FB!
Also talk about her emotions and motivations this really makes you important for her and if you keep the sexual tension up things will go the right way.
But for real, sexual tension is the fundament, otherwise your faster in the friend zone than a guy dude!