so after played a few round of pirate pq, there are many problems: -bellflower concentrate not dropping? or just rare. The Ginseng one dropped frequently, but not Bellflower and they don't even drops in the invisible bellflower room at stage 3 or 4 optional stage. -optional room at stage 4 only allow one person to come in. I don't know if this is a bug or how it always been, it needs to be checked. -lord pirate hook never drop. Like there are quest that stated it needs like 20 of them. How am I ever gonna finish the quest if it never drop? -as well as the lord pirate key. Some of the members in my party confirmed it did dropped, but only on super rare occasion. Just a minor complain really.
Has already been reported and is being fixed in the next update. Not a bug. I assume you mean the quest "An Evidence of Slaying the Captain" which has nothing to do with PPQ, and drops from regular Captain monsters. Not a bug.
There is one other issue as well, the follow up quest to "An Evidence of Slaying the Captain" requires you to obtain an item "Lord Pirate's Travel Diary" and that one does not currently drop in PPQ, will be fixed in the next update however.