Good questions modern.
You select a single mission and then that is the only one you can be on. When a mission is complete, it shouldn't disappear, it should remain on the list, but marked with a V. You know like _/ or something, it's hard to type on a keyboard
You can't quit a mission that you are currently on. That would answer the last question too.
EDIT: By reading your posts, playing WoW and answering your questions, i got an idea. What if the "Main Leader" NPC transported you to different areas, and you could get quests from npc's in these areas? If you have ever played WoW, you know what i mean.
It would be quite simple actually, and could be done mostly with events. The only thing that would need to be scripted would be a quest log/journal. Because you would get the quest from an npc, activate a switch, and that switch would make her say something like "finished yet?" and update the quest log. When you are then done with the quest, you would activate another switch which would update the quest log to say "Complete" and make the npc finish the quest. Then, when you are done talking to the npc the quest would vanish from the quest log, and the npc would just thank you or something whenever you came by.