QIf I put an enemy follower from the field into the EX area, does it lose all its counters?

AYes, it does.

QIf I move an evolved enemy follower into the EX area with this follower's Fanfare ability, do both the unevolved and evolved cards get put into the EX area?

ANo. When an evolved follower is put into the EX area, only the unevolved form stays in the EX area. The evolved follower is moved faceup to the evolve deck area.

QIf I put an enemy token follower into the EX area from the field, is that token follower removed from the game?

ANo. Tokens can exist in the EX area.

QIf I put an enemy follower into the EX area with this follower's Fanfare ability, does it lose any damage and abilities applied to it?

AYes. When a card is moved from the field to the EX area, it loses all damage and abilities that were given to it.