Can I let my eleven year old daughter be friends with a guy if he's seventeen and they only talk through the internet? They met online. He's seventeen and thinks she's fourteen. It seems he is her only friend and she seems so much happier talking to him.

I would question why a seventeen year old wants to be friends with an eleven year old online.  The age differences makes something smell fishy.  

Besides, there are a lot of things he could persuade her to send him sexual photographs of herself or even to try to meet up with him.