I think it was meant to be "O quarto está vazio", because its the state of the room.
But the room can not change its state on its own and would remain like this forever?
It's sort of....
When one sets the things at their places in his room, they hardly change. So you often go to your friends house, and his bedroom is always the same. (Ok, it can change, but it's rare). That's why "é" is used in this case.
Actually it is very uncommon to say "O quarto é vazio" in Portuguese, it doesn't make much sense to talk about a room that is empty by nature. If it were the inverse translation I would definitely say "o quarto está vazio".
I've seen Duolingo mistakenly putting "é" instead of "está" a few times already. It's not completely wrong, but it changes a meaning to an extent that it becomes a weird sentence.
The meaning with "é" would be something like "the room has few pieces of furniture".
Why is "o quarto" the bedroom in this sentence and not just the room? Shouldn't bed room be o quarto de cama or some thing to that effect?
I'm not sure but I would think because all the other rooms in a house have specific names. Cozinha, sala de estar, sala de jantar, banheiro. Sala is used for room with a specific name type. Quarto means an actual room where one sleeps.
One can say «quarto de cama» for "bedroom," but we normally just shorten it to «quarto» in everyday speech. It becomes extremely easy to know that one is referring to a bedroom when you use a possessive, too: «no meu quarto...» = "in my bedroom...." Obviously, in English you can say "my room," and you do not have to specify "my bedroom," either.