Translation:I will explain everything to you at lunch.
I would say "okay", but not totally correct. Slight difference there. "at" is a bit more time-thing. That could mean that you explain it, when it is lunch time and you meet the person in the hallway. Whereas "bei" means that you are explaining it when you are having lunch.
Small thing. I would accept yours too.
I find it strange that the dictionary hover of "beim" is "at" or "with the" yet the English translation of the sentence chooses to use "over". "I will explain everything to you at lunch" has an identical meaning and would probably be my preferred way to say the sentence as a British native.
Seems unnecessarily confusing, particularly if you're not a native English speaker, whereas it doesn't change the German. It managed to trick me in the "pick the correct translation" version.
In speech it would be context, that gives the you or them. Written, it is Ihnen (uppercase I) for you and ihnen (lowercase i) for them .
Because that just doesn't work in English - it needs to be "explain everything to you". I suspect the reason is that German, and other languages, clearly have "you" in dative, so the "to" can be left out - but in English, "you" is the same in every case, so we need the "to" (or other appropriate preposition) to clarify.
"At lunch" is an adverb phrase, so it must be placed after the verb it modifies. You can make it work with commas, e.g. "I will, at lunch, explain".
"To you" is an indirect object, so it should normally go after the direct object.
English has rules about word order, and they don't make sense at all.
Every language has rules about word order. If you grow up with a language, the word order makes perfect sense. Granted, a lot of rules in English are made to be broken, but that is the reason we study languages. I, for one, don't want to speak "pigeon-German" or "pigeon-Chinese." Maybe Duolingo doesn't list all the possible ways of saying something in English, but we're here to learn German!!
Yet again Duo marks good English wrong: https://screenshots.firefox.com/csBJW33wP7PpiJtE/www.duolingo.com
It could be possible, did you report it? A word of warning, Google translator is not a source to trust for referencing languages or translations. It might get the general idea correct and that great, but it doesn't identify incorrect prepositions or grammar errors and so on.
That is a very awkward way to word it.