I want to explore the omen islands. :)

Also, what happens when I complete a treasure map?

Hi! If I'm not mistaken, you can find Uncharted Land Map pieces through Random Events. Or, you can buy them from user shops. They were also given out in an event a few years back but aren't obtainable in that regard anymore.

When you complete the Uncharted Land Map, you get access to the island, a special vending machine that vends clothing called Ocean's Depths, Merana if you want to get a hydrus pet, and Port Plunder. In Port Plunder, you get access to Drunk Carl's quests and the Galley.

When you complete a Treasure Map, you get a prize! I believe it is sP and some items. It also gets you one step closer to gaining access to the Blue Building.

Uncharted Land Map pieces come through random events. You can also buy them from other users (who got theirs through random events). The Uncharted Land Map is not the same as the Treasure Map. The Treasure Maps game is old and I think it misnames them or something?

Completing the Treasure Map is one of the things you need to do to get into the Blue Building. This is the main reason for doing this. I think you get some sP and a few rare items when you complete it, but it's been years since I have done so so who knows what happens now. It used to be true that the items and sP didn't usually compensate you for the cost/selling price of the pieces.