We've been complaining about pirate ships not working right since the game went live. Noone, as in Devs or Cal have given any kind of responses at all yet. There are a few threads written about pirate hunting and the ships not taking damage, it is also listed in bugs at top of UHall.
As far as the quests go... the quest is not for a specific pirate. There is a bullitan board by Bigsby, and it could be any of those pirates listed, and the list may change from time to time. So basically capturing or killing any pirate will work. They will hark some clues as to where to find a pirate, but it does not matter if that is the one you capture or kill. They will often move by the time you get there or the names may have changed, or someone else may have taken it out.
At one time, I thought maybe the reason we could not damage a pirate was because we did not get one that was on the board, so I went back to board, wrote down a list of them, by time I got back to where the pirates were located, all the pirate names had changed again.