Do you think she is a fake person (Facebook) ?

[ℰℓℓℯ]

Would a female do such a thing? It happens. The anonymity of the internet makes women "dare" a bit more than in real life. It is as you say, you'll never meet so she doesn't have to worry about that. She can do what she wants without any repercussions.

Could it be a guy? Maybe. That happens too. There is no way of telling though, not from what you wrote here.