She googled her name and found the forum. If you found people discussing you on a forum, you might join to set the record straight.
She realised Alex was even creepier than she had thought, and that regardless of what she said he wouldn't accept that she had no feelings for him, so she left.
She stares at him, either because she's giving him a look telling him to "fuck off", or she sees him as a freak and is fascinated by him in the same way you might be fascinated by a dude with no arms and would stare at them, or she's actually afraid of him so wants to ensure she knows where he's at when he's around her.
As to her laughing, she either laughed at him cause he's so pathetic, or laughed at the ridiculousness of the situation, the fact that he still hasn't got the message (that message being that she really truely doesn't like him) even after she's made it so damn obvious.
She probably told you to leave cause she doesn't like you, cause your Alex's friend. Or maybe she thinks your spying on her, as you report everything she does to him.
