QIs the card put into the EX area by this follower's ability treated as permanently costing 2 less even after it's put onto the field?

ANo. The cost reduction only applies when playing the card.

QIf I put a 1-play-point card into my EX area with this follower's ability, does it cost 0 to play?

AYes. Cost cannot be a negative value, so it would cost 0 play points.