It was suggested on a different thread that there is a subtle difference between: "Magst du mich?" - Do you like me? and "Du magst mich?" - You like me?
In english the second question suggests surprise/incredibility (it would probably have conversation preceding it) while as the first one is a straightforward question. I'm guessing: "Mag sie dich nicht?" - Doesn't she like you? (basic question) "Sie mag dich nicht? - She doesn't like you? (really a statement made into a question and would probably suggest surprise, similar to "you like me?" above)
You need to look at the word forms here, German depends more on declination and conjugation that word order.
For this sentence there are two things you can look at: The declination of pronouns --> dich is the accusative case of du, and so in this sentence can only be the subject (the one who is liked). Sie is a little more tricky since it has several meanings (but they are all nomative as far as I know) but we can look at the main verb ( usually found in th first position when there are no question words). Mag is either the ich or er/sie/as form of mögen (it would be "magst du ..." In your sentence) so we conclude that it must be she, not you formal who is the one doing the liking or not.
You need to use the accusative case.
"She don't like you" is grammatically incorrect English. If your first language is English and you don't know that, you didn't pay attention in school. If English is not your first language you also didn't pay attention in school. If you didn't go to school to learn English, whoever taught you English didn't pay attention in school.
What's wrong with the construction of this sentence? It seems fine to me. 'Sie mag dich nicht' - She doesn't like you. In German, to adapt the sentence into a question, the subject/verb order is inverted (mag sie dich nicht?), which in this case asks, 'doesn't she like you'?
This construction is typical of adapting statements into questions in German.
Google translate is a very unreliable method of finding accurate translations. It's useful for getting the general feel of something, but it shouldn't be relied upon. For 'they', 'mögen' would have to be used rather than 'mag'.
If there are disagreements between Duolingo and Google Translate, I'd be pretty confident that it is Google Translate's error most of the time.
English is a highly personalized language. I say a good English teacher should be a historian as well to truely know what the language is in it's use across the world. I'm from Bermuda (UK territory) and we have words and expressions that is uniquely an expansion to the it.