QIf my EX area is full, can I still play this follower's Fanfare ability?

ANo, unless you can put a token follower from your field into another player's EX area that isn't full.

QIf I put a follower into the EX area with this follower's Fanfare ability, does it lose any damage dealt or abilities given to it?

AYes, it does.

QIf I select a token for this follower's Fanfare ability, does it get removed from the game?

ANo. It remains in its owner's EX area after you put it there. Follower and amulet tokens may exist in the EX area, field, and resolution zone. They are only removed from the game immediately after movement to other zones.