"Whose coat is it?" should be accepted. "Whose is the coat" sounds a bit less natural to me as an English native.
This sentence literally translates "Of whom is the coat?", which is grammatically correct but was marked incorrect. This translation is almost never said in conversational English anyway. However, the translation "Whose is the coat?" is NEVER said in English. "Whose coat is it?" should be the correct translation.
I wouldn't say never. I'm English and would definitely say "Whose is this drink?" For example