Does the ship itself have to take an action to fire its weapons, or is that seperate? Can a ship double move and still fire its ballistas or whatever?
According to the players guide, a ship cannot actually make a "Double move" A ship can move no faster than its top speed, and it takes a standard action to accelerate to a faster speed, so as far as I can tell, no a ship cannot fire its weapons after doing a maneuver such as Full ahead or Hard to Port/Starboard.
However that being said, a PC on the ship who is controlling a weapon can make an attack on their initiative with the siege weapon.