"Do we have doors?"
Translation:У нас есть двери?
I would say that you can hear "Есть у нас двери?" form of a question from an annoyed human being. In that case it is likely to end with "?!". But! If one is a sarcastic person with a little irony obsession he or she can pronounce it without extra expression in which case you would probably feel the patronizing pose towards you. It is no wonder that you can't find that kind of information in the begginer's course. P.S. The famous Russian grammar "freedom" doesn't give you a right to say any random word sequence and actually deliver the message. It is a bit frustrating. But there is a reward: you can understand something about your conversation partner based on how he constructs his sentences. Interesting, isn't it?
Literally speaking, Russian doesn't make that much use of “X has Y” construction — will rather say “at X there is Y” (X has Y at his disposal), which is «у X-Gen есть Y». But, as you probably know, the preposition «у» needs the Genitive case, and the Genitive of «мы» is «нас».
Без "есть" может прозвучать, но как недоумение или сарказм. Вот в этом "доме" http://svoyabesedka.ru/wp-content/uploads/ne-mudrstvuya-lukavo-mozhno-oborudovat-kuhnyu-sovsem-bez-sten-a-v-sluchae-dozhdya-ustanovit-naves.jpg сын спрашивает у отца: Папа, а где у нас двери?
Отец отвечает: У нас двери? Да у нас и стен-то нет.