1) Is it a square adjacent to the Battleship or to the target ship?
Move to an adjacent square to the target.
2) If it is a square adjacent to the target ship, can the target ship be moved 3 spaces away from the Battleship?
Yes. It can be pulled or pushed.
I think by "applicable" they just mean any space that is legal for a ship to be moved into. You couldn't move it into a space with enemy ships, or a space where it would exceed 5 points of your own ships.