1. Yes, you can still move the navy that didn’t participate in combat into and/or through the sea zone during non-combat move. Once all the enemy ships in a sea zone are destroyed, the sea zone is no longer considered hostile and there is no restriction of movement into or through it during non-combat movement.
Also remember that you can ignore enemy transports and submarines when moving through sea zones. They don’t make a sea zone hostile.
2. Yes, they can.