In a barrel we found a 'Key' ('Open 1 Door or Chest without rolling dice.'). We used it to open the door at point 2 with it. The door with the 3 different locks. Was that allowed?
It wasn't but it's not your fault.
There's a completely wrong line on the mission.
Any magic door (e.g. non-standard door) cannot be opened via items, equipment or bypassed with any special power (Barka's catapult move or Yang Ping's shadow step). In mission 3, also, the additional difficulty of the roll to open the door applies also to strength rolls.