It is a question in English. The translation doesn't take American English idiom into account sufficiently - we'd normally say, "Do you that THAT she has THE/ANY answers?"
"Do you think she has answers?" is actually very peculiar and odd English. Even a bit weird.
"Do you think (without "s") she has the answers" should be accepted. Report it next time.
In my experience, there are no set rules. This is purely idiomatic, and applies to a lot of verbs. "Говорите по-русский?" for instance.
Looking at the Russian and English as I see them at the top of the page--
"Думаете, у неё есть ответы?" Translation: Do you think she has answers?
--I would say no. "Do you think has she answers" would not be correct English.
You could make the case that a standalone sentence, "Has she any answers?" or "Has she the answers?" would be correct - note that it sounds more formal to my ear, and would be probably used more widely in British English rather than American English. (I do not imply that one is more correct over the other - I am simply distinguishing regional differences as I see them as a matter of trivia/interest. Both uses would be perfectly understood in either location.)
However, the main part of the English sentence is, "Do you think", with an understood/omitted "that", followed by "she has answers" at the end. So in other words, the main clause is Do you think, followed by the subordinate clause, [that] she has answers. Subordinate clauses that start with that (or clauses which could use that but omit it) do not use inverted word order such as "has she" and instead must say "she has." Inverted word order is when the verb precedes the subject of the sentence.
I'm not sure if you are taking issue with the absence of "that" from Duo's translation, or the absence of "the/any" from "answers" - or both.
Duo's translation is not incorrect English, it's just peculiar, less so regarding the absence of "that", more so regarding "the/any". Duo's translation comes across as highly stylized, with a bit of a dramatic flair. It's plenty weird.
Unfortunately, misunderstanding often happens even between people speaking the same language.
ты думаешь - informal singular
вы думаете - plural, or formal singular/plural
Also: These are NOT the imperative forms of the verb; those are (Imperfective aspect):
Don't ask me what Imperfect Aspect means - I haven't gotten that far yet; I'm merely copying these verb-forms from a conjugation table, and I think it's a good idea to get things right the first time, even if you don't yet know what they signify.
This thing really has trouble enunciating certain sounds so that they don't sound identical - неё should not sound like него
Такая форма вопроса подразумевает,что у нее ответов нет и в этом следует убедиться. Вот что это значит на русском. Создатели курса, обратите внимание на мнение народа. Возможно несколько вариантов перевода, но другие правильные ответы не принимаются. Иногда эта тупость бесит,особенно, когда приходится по несколько раз вводить ответ. Это заставляет пользователей обращаться в Гугл ,что многие тут и делают. Я также столкнулась с тем, что английский и русский являются государственными и разговорными языками в разных странах, и различия могут быть существенны. Но люди понимают друг друга. Почему создатели курса не прислушиваются к носителям языка и не учитывают их мнения?