"The Korean man is walking behind the Indian woman."
Translation:A koreai férfi az indiai nő mögött sétál.
Sure, it's fine.
Your sentence would answer the question, "Who is walking behind the Indian woman?"
The other version, A koreai férfi az indiai nő mögött sétál would answer the question, "Where is the Korean man walking?" or, "Behind whom is the Korean man walking?"
Ki sétál az indiai nő mögött? A koreai férfi sétál az indiai nő mögött. Look right before the verb in the question and answer: Ki? A koreai férfi.
Hol sétál a koreai férfi? A koreai férfi az indiai nő mögött sétál. Short version (right before the verb): Hol? Az indiai nő mögött.
The word order you choose for your sentence is partly determined by which piece of information you are trying to communicate to the listener. That important "focus" item has to come immediately before the verb.
Yes, both should be accepted and it's not possible to choose between them based on the English sentence alone. I'm pretty sure they began these exercises with the Hungarian sentence, and provided several English translations, but didn't always catch all the ways those could be translated back into Hungarian (especially different word orders).
Yes, that's how Duolingo works.
It's a bit unfortunate, sometimes, because sometimes you would like to provide exercises for multiple English sentences to translate into Hungarian (or Klingon or whatever), but for each Hungarian sentence, you can only have zero or one English-to-Hungarian exercise, which is automatically generated from the first possible translation of the Hungarian-to-English exercise.
So if you want to practise English-to-X translation with differing word orders, you have to make one X-to-English sentence for each thing you would like to focus on.
(For example, Klingon doesn't have verb tense, only aspect, so there's no way to create, say, two English sentences "Mara flies" and "Mara flew", since both of those would translate to puv mara but there can only be one English exercise associated with that. So I'd have to make, say, two sentence such as puv mara and puv torgh and make the first translation "Mara flies" on the first one and "Torg flew" on the second one, if I want the users to practise translating simple past to the unmarked aspect.)