It is passive voice, because the verb "to be" is used. In this context open and closed are adjectives, not verbs. "Closed" and "open", when used as adjectives, explain the situation properly. "Close", as an adjective, means near. These 3 words can be used as either an adjective OR a verb. So, you have to look at usage/context to know which it is and then you will know which rules to apply to using the word open. "Opened" is only used as a verb (source: dictionary), so it wouldn't be used to describe a noun. Examples: Adj - The door(noun) is(passive verb) open(adjective). Verb - The door(noun) is opened(passive verb) by John. Verb - Open(command) the door(noun), John. Adj - The door(noun) is(passive verb) closed(adjective). Verb - The door(noun) is closed(passive verb) by John. Adj - The door(noun) is(passive verb) close(adjective). Verb - Close(command) the door(noun), John. I'm not sure about the linguistic origin but hopefully this helps.

There is no reason. This whole "open vs. closed" is the same for everything. Shops, minds, books, legs, bags, whatever. Any reasons other people give doesn't really take this into account. There's no real reason for it. It's kinda weird.

just because if the door is close it means that it was open before but now it is closed, because someone closed it severel minutes ago and we see it close... that is why we use "closed"... but if we see the door open we say that it is open because usually the doors should be open and noone opened it for us, it was just open... usually the doors should be open every moment

An interesting question. I do not know whether there is a grammatical reason for this or not... As far I know: it is a basic assumption that things, such as doors, holes, etc., are OPEN and that when they are CLOSED it is due to an outside power. In other words when "the door is open" is it because it is its natural state and when "the door is closed" it is because someone or something closed it.