I haven't done Facebook API stuff for a while but it used to be that the emails it would give you were @facebook.com proxy addresses.

It depends on their privacy settings if you can get to it or not through the api. Your app can request explicit extended permission for it. http://developers.facebook.com/docs/authentication/permissio...

I'm not sure, but perhaps a combination of the following: They would rather you message them through facebook, and they fear fake-profiles friending people at random and collecting emails to be used for spam, were a query possible to collect them.

Can't be done. At all. I've spent many hours trying.