1 - Quests in the areas. Normally you get sent from one hub to another, but that might not always be the case. Drybone is high-teens, so you might want to start there if you haven't already. I can't remember off the top of my head for Gridania or Limsa, might be Quarrymill for Grid.

2 - Mor Dhona, you'll get there story-wise after 40. You'll look for the tent everyone is gathered around, this's where you'll also exchange for Darklight and Mythic armor when you get Allagan Tomes once you hit 50. The person on the left is the one that does Swimsuit Exchanges, as well as Odin/Behemoth exchanges when/if you get the drops from the FATE mobs.

3 - Career DRG, I dumped directly into STR and only. I haven't bothered with any other experimenting myself.

4 - Duty Finder I don't think there is a way, but if you look in System... I think it was Character Settings, one of the menus should have a 'Recommendations on entering area' and click that. The Recommendations is for things like Quests, at-level Dungeons, Hunting Log mobs, FATEs, etc.