Hi Lyon'ka,
When we say "The door is closed", we are using "closed" as an adjective to describe the state of the door being shut. Another point to note is the fact that "closed" is an example of a participial adjective (verbs that end with -ed, -ing or -en but functions as an adjective). This is also the reason why we can say "The door is opened" to describe the position of the door that permits one to enter a room.
We are not using "opened" and "closed" as verbs here.
Other examples of participial adjectives include:
interestING, interestED (The lecture was very interestING (adj) and we were all very interestED (adj).)
On a separate note,
"The door is opened." and "The door is closed." are both in the passive voice. As such, someone has opened or closed the door previously. The identity of that person is unknown here but the meaning is still complete.
When we say "The door is close", we are also using an adjective, albeit with a different meaning. It means something in close proximity -- you are near the door.
Lastly, "The door is open" sounds odd. I would change it to "The open door", which means that the door is in a position (ajar) that permits access into a room.
"The door is opened." --Someone opened it, now it is ajar.
"The open door" -- The door is ajar. The focus is not on who opened it.
Hope this helps.
Cheers,
Lance