Conquest of Alligator Island
1) This quest starts in Heine in the Warehouse with Warehouse Frieghtman Kluck. He wants you to hunt the mobs on Alligator island, Crokian lads, Dailaon Lads,
Crokian Lad Warriors, Farhite Lads, Nos Lads, and the Swamp Tribe and bring back their teeth.
2) Basically all the mobs on the island give quest items, except maybe the Alligator which you can pick up Alligator Hunter quest for.
Sometimes you will also receive a Mysterious Map Piece, which is only good in sets of 10 for the Treasure Hunt quest.
3) When you have some items go back to Kluck and the most important options really are "I've brought you some teeth" where you get rewarded with a decent amount of adena. You get 220a per Alligator Tooth plus a basic bonus of 3100a starting from the first Tooth; if you bring in 100 or more Alligator Teeth, the bonus is 10,700a.
Or if you have pieces of maps in sets of 10, "yes it seems to be a piece of a map" which links to the quest I pointed out earlier. You can have multiple Pirate maps at a
time but can only use one at a time in Searching for Treasure, unless you sell them, which is dumb.