"Do the children usually eat Danish food?"
Translation:Những đứa trẻ có thường xuyên ăn thức ăn Đan Mạch không?
Why is the answer "Những đứa trẻ thường xuyên ăn thức ăn Đan Mạch không?" marked as wrong?
More generally: When do you use "có ... không?" in a question and when is "không?" sufficient as a question marker?
"có" is not mandatory, but leaving it out makes your sentence somewhat informal, casual, familiar. just be careful not to sound rude when talking with elders, strangers, and people of higher status, like your boss, your teacher, etc.
maybe because of some rhythmic reason, I feel it sounds much better and natural with "có" as given above than without it like in your sentence.