No. Once you confirm your fleet it is locked in for the whole game, so you cannot move or rotate a ship after placing it.
Your fleet is fixed once you confirm it. Before that you can arrange the ships as often as you like, turn them across or down, or use Randomize. After you confirm you are ready, nothing moves for the rest of the game.
Battle starts when both fleets are set
Nobody can fire until both players have placed their whole fleet. If you are ready first, you wait for your opponent to finish placing.
Is your fleet visible?
No. Your opponent only learns about a ship cell when they fire at it and hit, so an unhit ship stays hidden. Placing well matters because you cannot change it later: see the strategy guide for placement advice, whether ships can touch, and the full rules.