1) As Talion said dungeon queues are frustrating for dps without a tank/healer to queue with. To get 20 you would have to do FATEs and levequests or you could attempt at moving around the world on foot to find level appropriate quests.
2) You need to keep hold of them for now. Once you hit the 40s you can make a run for Mor Dhona, here there is an NPC that you trade them over to.
3) I'm not sure on the optimal allocation of attributes, if there even is an optimal set-up. My classes have all points into main stat, so my Lancer is getting all Strength.
4) Not sure you can get it to automatically pop on zone change but once in the Duty Finder it's added to the top of your quest log, you can click that every time you zone to check status.