No. Each cell on your opponent’s grid can be fired at only once, and a second shot at the same cell is refused. Pick one you have not tried.
You cannot repeat a shot. Every cell on your opponent’s grid can be fired at once per game, and the game refuses a second shot at a cell you have already tried, so you never lose a turn by accident.
Hits and misses stay marked
Both hits and misses are marked on the grid after you fire. Cells you have not fired at are the ones left to choose from, and your opponent’s grid works the same way for them.
Using that
With 100 cells and a repeat never allowed, a plan beats random guessing: fire in a pattern that cannot hide the smaller ships, then work around each hit. The Naval Battle strategy guide sets one out. See also whether you get another shot after a hit and the full rules.