It is a set expression. If you ask "как у тебя дела?" (lit. "How are things you do?"), you get "У меня всё хорошо" (the "stuff" I do is fine)—of course, if the answer is optimistic at all. ^_^
It works the same for anyone else.
"With the child everything is fine" is wrong: Very unnatural word order. Why is this wrong? Isn't this course about learning what the sentence means?
It is an odd wording but I do see where it comes from, that is how I mentally read this sentence structure. Rearranging it to "everything is fine with the child" sounds more natural to me.
The issue with such answers is, some of us are not native speakers of English (for example, I am not). I usually know a few typical ways of saying things but it is hard to imagine how an English speaker parses a very uncommon phrasing, something like "By me is a dog" or "With me all is well". Is it OK or might it be that the user failed to understand the Russian sentence? I am never sure.
I think it's better to go for the natural sounding response generally and then when people have gone a bit further up the tree, The sentence structure becomes clearer. If the suggested answer sounds unnatural the meaning of the sentence gets lost
Duolingo is rather inconsistent about these things. For some exercises a literal translation is allowed and for some it isn't; just keep reporting it.
It is sometimes allowed where it makes sense. Literal translations are generally not waht we do here, though literal translations of the whole blocks is OK.
"The child is doing fine" was not accepted. The suggested translation of "the child is fine" is a little ambiguous in its meaning. Is the the child safe and well cared for or is the person tasked with watching the child pleased that the child is we behaved and not causing problems? Or could it be both as in english?