My
1) Opening doors
I allow heroes and monsters to either open or close each door once in their turn. So a hero could open a door and see a room full of monsters but they would not be able to close it again in their turn, they could move to another square and the next hero could move and close the door though.
If you are adjacent to a door you can hold it closed to prevent monsters from attacking you, monsters can also do the same forcing heroes to move back so that the quest progresses.
Undiscovered monsters can't open doors unless there's some kind of ambush described in the quest notes. Discovered monsters can open doors to undiscovered areas and in doing so summon reinforcements, but I tend not to do this very often as it's not in the spirit of the game.
2) Death
We play that zero is dead too. That's what the UK rules say and I agree. My one gripe is that because the Wizard only has 4 body points he has to use healing potions and spells when he's at at least 1 body point, thus wasting a potential +1 body point, but short of altering the Wizards BP to 5, there's no way round this, because zero is dead, end of story.
Other heroes can pick up the dead heroes stuff if they want but I have limits on how many weapons each can carry so a weapon of some kind will nearly always get left behind. This prevents returning weaponry to the same player's newly created hero at the start of the next quest, and so gives death some significance.