Check out my Tips & note section in this skill. In yes-no question, "có" is there just to form the question. No meaning.
the "khong" at the end makes it a question. I don't think this was a fair question, because the "co" translates, as per the drop-down, to there is or there are, so it is logical to assume that the answer should be "are you eating chicken?" However, that is marked wrong.
I haven't started the questions skill, but I got this question during "strengthen skills". Is it miscategorized, or does Duolingo just give "advanced" questions sometimes?
Duolingo gives random questions in "strengthen skill" session. And it's possible that sometimes they give out questions that you have not yet learned.
You need không at the end of the sentence to make it a yes/no question. While they don't appear next to each other, có and không are paired words and both need to be in the sentence if yes / no. If not yes / no question, then rules can vary / change.
Not necessarily, plenty of yes/no questions given here that only have 'không' without 'có', so I think the confusion you see is understandable.
this is infuriating, because they wouldn't give the credit for Do you eat lunch, it had to be DON'T you eat lunch?! Now the exact same wording, and it doesn't give credit for Don't you eat chicken?!!!!! It has to be DO you eat chicken?!!! AAAAARRRRGGGGGHHHHH!!!!!!!!