"Do you eat a carrot?"
The English sentence "Do you eat a carrot?" is very unnatural. It should be "Do you eat carrots?" (in the habitual sense, in general, do you regularly eat carrots? do you like eating carrots?) or "Are you eating a carrot?" (right now). Saying "Do you eat a carrot?" implies that there is one carrot that the person eats throughout their life.
Yeah, it should be accepted. It must be a lot of work typing in all of the allowable answers for each question. Make a report if you get to this again. In fact, if you feel like helping out a bit, try with "je" in front of any yes/no question and report it any time it's not accepted.
I haven't seen it before question-word-questions.
Have a look through the translation database at the bottom: https://glosbe.com/sw/en/je
I think it's a way of making it very clear that it's a question when intonation is otherwise the only way to indicate it. If a question has a word like nani, nini, ngapi, gani etc., that word makes it unambiguously a question as well.