Okay, I’d like to clarify one thing - is there any difference between "nebo" and "anebo" except they sounds differently? Or can "nebo" be used both in yes/no questions and questions requiring a precise answer while "anebo" applies only for the second kind of questions?
"Je živý nebo mrtvý? " - the answer may be either "Je živý" or ""Je mrtvý", I can also ask: "Je živý anebo mrtvý?"
"Je bílý nebo černý?" - depending on the context, the answer may be either 'yes', 'no', "Je bílý" etc. "Je bílý anebo černý?" - the answer may be only 'yes' or 'no'.
Or is it the other way around or is intonation the only way to mark the kind of answer we expect?
In my opinion, it should not be accepted. Even though your translation would be the correct one in some real life occasions, in a language course, it is important to teach the students to pay attention to the gender. The only way of achieving this in duolingo is to insist that the grammatical genders are translated literally (unless there is additional context).