Sometimes Facebook requires a photo ID to be submitted before "approving" a new account. Seems to happen when they suspect the person isn't real (fake name, or whatever).
not good enough. maybe if you only play solo games, but once you play with others facebook will get enough data to get an idea, if not identify who you really are. you may get tagged by your friends or family, connected to a location, etc, many ways to leak personal information. the only way to stay safe is to not log in to facebook