There is nothing adolescent about chlapec. They are completely interchangeable. The use depends mostly on speaker's location. Chlapec is slightly more 'proper', used more in Moravia. You would rarely hear it in Prague outside of media. Hoch is archaic but again might be used at some locations.
The singular they is extremely confusing when used in language courses unless used in sentences where it makes a clear sense. Learners WILL get confused by that. That does not have anything to do with the fact whether the authors of this course personally do or do not use singular they .
I am not aware of any language corpus that would support a significant usage of singular they in this sentence, but you are welcome to show otherwise.
Duolingo gives "which", "what" or "that" as translations of "co". "What is that," would be a very rude way of saying it, so "which is that" would be better English unless the Czech is intentionally rude, which I don't think is the intention... so I reported it as a problem
@ JohnFKoen Not all languages are like English. In both German and Czech "the child" is neuter/it, has a neuter article. You do not use masculine or feminine articles, or pronouns, when speaking about a child unless you are speaking about a specific gender. Such as "the girl", "the boy"...
I'm an English teacher and a book editor. I have a large number of books on grammar and style, which in the course of editing books I have read thoroughly. So my source is myself, and my accumulated experience, but if you have a good argument for why "Which is it..." should not be accepted, I'd be happy to hear it. I didn't say that "What is it" is incorrect, but it is awkward.