Enemies you have seen are shown as portraits at the top right. Hover over them to see how far they can move in one action.
Doors obstruct movement for both heroes and monsters until they are opened.
If monsters have been woken up by an alarm, they'll break down closed doors between them and the source of the alarm.
At higher difficulty levels doors have a chance to start open. There is also a combat modifier that affects this: Anticipation (all doors begin combat open).