2
I think you have to make some actions as in /include/checklogin.php
I think you need also a user created for the Facebook group and log in that one by the FaceBook login check.
Be very careful with the permissions for this group, since everybody can login on Facebook, you are introducing a second anonymous users group! Except that they may see more of your site, they shouldn't have no more rights on your site especially for posting etc, then the anonymous user.