This treatment of "have" as auxiliary when it means "to possess" is dialectal. If I recall correctly, people in North of England or Scotland may say that. In more standard varieties it would be a normal verb, so you would use "doesn't have".
Well, Wiktionary says that dach means roof and sufit means ceiling. A roof is visible from the outside looking down, and a ceiling is visible from the inside looking up. The roof and the ceiling are usually different surfaces.
"My room has no cieling." Is a perfectly acceptable answer. I've been using this construction all my life in the New York area. I have a masters degree in neurolinguistics from Bowling Green State University and used to teach ESL as well as freshman writing composition.