QIf the selected enemy follower's owner's EX area is full, can I still put it into the EX area?

ANo, it remains on the field.

QIf I put an enemy advanced follower into the EX area from the field, do I put that follower faceup on top of its owner's evolve deck?

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

QIf I put an enemy token follower into the EX area from the field, is that token follower 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 put a follower into the EX area, does it lose any damage dealt or abilities given to it?

AYes, it does.

QCan I play this follower's activated ability multiple times per turn?

AYes, you can.