Landing on an island from a sea zone requires movement of 1 space. Landing on the coast from the sea zone adjacent is a move of 1. Landing on a carrier in the same sea zone is a move of ZERO.
Also, you are NOT required to keep the AC alive during the battle until after the FIGs are dead. You are required to have a place to land your FIGs at the START of battle. If that landing zone gets sunk during the battle, the FIGs can fight on until the bitter end, and then they go “SPLASH!” into the ocean, unless they have enough movement left to get them to another LZ.