Does Heimerdinger get exhausted and pay mana costs when using abilities he gains, or does he just have the ability without those costs?

Ruling: Heimerdinger has the ability and must pay the full cost when he uses an ability, including exhausting.

Nuances:

• If Heimerdinger uses an ability with a reaction tag (like Kai'Sa's ability), he can use it at reaction speed even though Heimerdinger himself doesn't have a reaction tag, because the reaction tag is on the ability itself.