"Do the children usually eat Danish food?"
Translation:Những đứa trẻ có thường xuyên ăn thức ăn Đan Mạch không?
"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.
But there are a good number of other expressions that just use 'không'-- some of these, if they use 'đang', 'đã', 'chưa', or 'sẽ' Huy has explained, but others the 'có' is dropped for no apparent reason. And we newbies can't go by how it 'sounds' to a native speaker. We need clear rules.
But you said it wasn't wrong, just awkward. At this level, just not being wrong is our goal. Nobody who completes this course and even knows its full content by heart is ready to step out and converse with a Vietnamese person on the street. People who think they will be are kidding themselves.
It's the same for my Vietnamese friends learning English. Even though sometimes they construct English sentences that aren't the King's English or sound a bit awkward if they got across their meaning then they're good. They often say things like "Today we have rain" which is unusual, even awkward English (but not wrong) but all English speakers can understand their meaning. It's only when they are writing papers (I have proofread a good many papers for a professor friend in HCMC to be published) is when I pull out the virtual red pen and re-phrase their writing to make it sound more natural.