First of all, I keep getting stuck with parties who either can't get past the first sub boss or I get thrown off the quest. This is happening way too many times for me. Is there a way to avoid the Doom spell? And where is the Wardstone? I see a green arrow on the map, but when I go down the stairs to find the second sub boss (the Rock Golem), the arrow disappears. Could this be the reason U get kicked off the quest, because I was suppose to find the Wardstone on that floor?
Whenever a quest instructs you to do a dungeon, you never have to do anything special in the dungeon to complete the quest. You just have to complete the dungeon. You will get quest credit either immediately upon boss death, or upon exiting after boss death. This holds true for quests that want you to obtain something: the required item will be added to your inventory automatically when you exit.
In re: Doom, cleanse it by stepping on the glowing tile. Make sure the status disappears from your bar. The light moves around, and you might step on the tile just as the glow moves to another tile, so don't stop unless you see it cleansed.