Pages should (and can) never send an individual message to a specific fan, the fan has to initiate the communication. It would be a major spam and privacy issue.
There is also no code to add someone as a friend, especially not triggered by new fans of a page. You can only open a dialog for a friend request: https://developers.facebook.com/docs/reference/dialogs/friends/
There are Realtime Updates, but not for fans: https://developers.facebook.com/docs/reference/api/page/#realtime