I personally feel all cannon ammunition should be limited. I read somewhere once that HMS Victory carried something like 27 tons of ammunition, which comes out to about 46 broadsides (or 23 volleys of all guns on board), assuming there were equal amounts of shot available for each class of cannon on board.
Repairs below the water line would've been done during battle, but actual repairs to hull damage that had no risk of causing the ship to take on water would've waited until afterwards. I can imagine some measure of repair may have been done to the rigging during battle, but sails weren't going to be patched and the man-power intensive task of setting a replacement mast sure as heck wouldn't have happened during battle. If it were up to me, emergency repairs would be the only thing available in the battle, with repair kits (rigging parts, sail cloth, oakum, planks, and fir logs) available once one leaves the battle instance.