In the passive (1), someone opens the door: the door is opened by someone, but you haven't mentioned who. In the intransitive active (2), the door did something: it moved to an open position, perhaps because of the wind, or perhaps because of a human action, but the basic idea is that the door moved. (3) is not a correct sentence.
4. Which door is open?
(4) is about the position of the doors now. One of them is in an open position. This sentence does not care about when the door moved, or who moved it, or how it happened, only on what it looks like now.