AndrewAAGamer is correct regarding LHTR, but it’s different in OOB.
In scenario 1, you may legally do as you propose. There is no rule that would prevent it. Of course, the carrier must survive the battle, or the fighters will be lost.
In scenario 2, the fighters may not move in noncombat movement after the carrier retreats. In order for a fighter on a carrier to move in NCM, it must launch before the carrier moves. Retreat is a type of movement. Normally, if fighters on a carrier want to move in NCM when their carrier makes a combat movement, they must launch in CM and remain in the sea zone, but in this scenario if they did so they would participate in the battle and would not be eligible to make a noncombat movement (though they could, of course, still land after the battle).