Are we allowed to gather any supply, gunpowder or Collector's chest before starting a Tall Tale ? The rules don't specify it so I suppose it's ok.

In Tall Tales n°9, the door to the underground can be left open by another crew (or yourself during a previous attempt). Is it ok to simply skip having to open the door or should we still be required to canon over to the statue and drop down even if the opening mecanism was already activated ?

Some Tales might better to speedrun than others. There's not that much rng involved with Tale n°1,6,7,8 and 9. To me the most interesting Tales to speedrun would be the n°1 (Shroudbreaker), n°9 (Shores of Gold) and n°7 (Fate of the Morningstar).

Tale 7 is the fatest completable tale in the campaign, well under 5 minutes with a brig or gally crew. Actually it's so fast that it could be the most reliable way to farm gold on a server.