I noticed that the very first campaign mission in D2 is there, but do they disappear after completion like regular games? Or do they stay there so you can replay it like the adventures do? And how do I locate quests that I have tracked?
Do campaign missions disappear when I complete them?
Yes, the missions will track on the Director until they're all done.
Where are my quests?
In the Quests tab of the main screen, where you find the Map, Destinations, and Store tabs.
How do I replay the campaigns?
If you go to the Tower and visit Amanda Holliday in the Hanger, she has quests which re-start the campaigns for you.