Omitting 'do' in English is like omiting pronouns in Russian: it's acceptable and pretty common in colloquial speech, but generally considered a less 'correct' way of speaking. Duolingo generally doesn't allow such variants.
(I'm not a native speaker of English, so correct me if I'm wrong.)
It actually has a shade of different meaning:
-"Do they believe you?" is asking a yes/no question
-"They believe you?" is assuming the belief, and asking for confirmation or elaboration on why
I'm not sure exactly why, in this case... but this sentence seems to be triggering this interpretation for many of us English speakers.
I think either is acceptable and correct, "Do they believe you ?' maybe just a fraction more formal. 'Omitting' has two 't's though, to rhyme with 'committing '; not that English follows its phonetic rules very religiously, but '-iting' would rhyme with 'biting' or 'fighting ' .
It is in the intonation. Which TTS engines often get wrong for Russian.
The most typical examples of Russian intonation are as follows:
- in a declarative sentence the pitch falls at the end (listing items, logical boundaries etc. are generally associated with rising intonation)
- in a yes/no question the intonation has a sharp peak on the core of the question, then falls. The core is the thing your yes/no is about (e.g. Ты ДОМА? or Ты вчера БЫЛ дома? or Ты вчера был ДОМА?). To be more exact, the stressed syllable of that word is going to be the highest, and then the voice plummets.
- in a question with a question word we also have a weak peak but don't let your hopes run too high.
Here I recorded some sentences. They are all questions.