QIf I put a follower into the EX area, does it lose any damage dealt or abilities given to it?

AYes, it does.

QIf my opponent's EX area is full when I select an enemy follower for this follower's Fanfare ability, what happens?

AIt remains on the field.

QIf I play this follower's Fanfare ability targeting an enemy token follower, 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.

QIf I play this follower's Fanfare ability targeting an enemy advanced follower, does it get put faceup on top of its owner's evolve deck?

ANo. It remains in its owner's EX area after you put it there.

Advanced followers may exist in the evolve deck area, field, EX area, and resolution zone. They are only put back onto the top of the evolve deck faceup immediately after movement to other zones.