"Sleeping room" is not natural English, unless you're talking about something special (such as a room in a sleep clinic where doctors study you while you sleep).
The room where you sleep and have "fun times" with your partner is called a bedroom.
(I am a native speaker of English.)
Which word is emphasized here? Is it that we don't sleep in the bedroom or that we don't sleep in the bedroom? And how would you say the one it's not in Polish?
It seems like a "normal" sentence, without "special" emphasis on anything, but I guess you say it with emphasis on "w sypialni". The only other way is "w sypialni nie śpimy" with emphasis on "nie śpimy".
You can also add "my", which always adds emphasis on "we". but
"W sypialni nie śpimy my" is more like somebody else sleeps in the bedroom, not us;
My nie śpimy w sypialni is WE don't sleep IN THE BEDROOM
My w sypialni nie śpimy/W sypialni my nie śpimy is WE don't SLEEP in the bedroom
we can also have bedchamber.
Given that noun words change with case, and that there are quite a few versions of each given word, which do not always follow the same rules of declination, can native speakers often or sometimes not know the right noun word for a given case, especially is that word is rarely used?
Yes. We have 'questions' that we learn in primary school, questions asked with every case, and we try to find similarities. Usually works easily, but sometimes we can still make mistakes.
No, it's Locative, as needed by 'w' = 'in'. Although Genitive would look the same.