Can you play berserker and then exchange it with changing or trader when you gain a berserker? It is effectively being gained to play, and gain to hand can be exchanged.
No. Berserker is not effectively being gained to play, it is gained normally, and then played from your discard pile. After you gain it and it is in your discard pile, you have 2 options:
1) Play Berserker. It moves to in-play, and then when you try to use Changeling to exchange it, the exchange fails because of the stop-moving rule.
2) Exchange Berserker for a Changeling. The exchange succeeds, and then you try to play Berserker but fail to do so because of the stop-moving rule combined with the new rule that says you can't play cards that can't be moved into play.
Under the old rules, you could exchange the Berserker and then play it, it would get played but stay in the supply pile. But new rules say you can't play a card which can't be moved to in-play.