Thanks for playing it!
1: Your roll Survival for traps. If you have the Traps tag, you hit on a 4, 5 and 6.
2: Traps only have effect if not deactivated. A gate can be opened if you find a key (it's in the treasure column).
3: Basically, yes. You need qualified staff for certain activities.
4: When you have nowhere to go. If all the corridors are explored and have an ending. The dungeon is done