Maybe the children learn from older children, who pass the grammar down over the years. I'm basing that partly on the idea that the older children would be part of the linguistic environment, and partly on reading about Nicaraguan Sign Language, which has been/is being created almost entirely by pre-pubescent children.

If the children aren't expected to use the indirect phrasing, and aren't corrected when they do ask direct questions (picked up from older siblings, cousins, or playmates), the younger children will learn two ways of seeking information, the direct question and the indirect and oblique "it would be good to know." They might gradually get the idea that one is "the way grown-ups talk," so along with being formally taught polite speech, they might gradually start imitating it in order to be seen as more grown up.

That makes sense.

Well... that might be a big hole in the world building.

But it might also be that children (maybe just one's own children) are normally asked questions, whether as part of baby talk ("Who's my big (girl/boy)?") or teaching ("did you remember to wash your hands?").

I think that if humans tried to emulate something like this, it would be very much a conscious, careful choice so that it's obvious how one *could* ask a question - but one just doesn't do that.

Not all languages have question formation as convoluted as English does; both Chinese and Japanese have the equivalent of "It is raining outside [question mark]", and in Japanese at least "It is raining outside [rising intonation]" is understood as a question even without the question particle at the end. If the elven language is similar I would guess that it wouldn't be hard to pick up how to form questions based on that.

...OTOH I'm having a really hard time imagining mothers asking their toddlers questions, or giving their toddlers instructions, using those kinds of oblique phrasings. I know of languages that are oblique like that in very polite contexts, but not of languages that are oblique like that even in intimate family conversations.

Two possibilities:
1) Children are asked simple questions because they are not yet expected to understand complex sentences. It's not so different from what we do with children.
2) Children learn the basic parts of a query and mimic what they can: subject and interrogative predicate. Formalization comes later, through further exposure.

Having never read the fiction in question, I find myself curious as to the motivation for the custom of indirect inquiry - was it ever clarified why that was considered more polite? (Was it that the other person in the conversation was thereby given the option of choosing not to answer, without it seeming as confrontational as might be the case if a question had been more directly posed?)

You are precisely correct -- in the society as described, a direct question is seen as rude because it forces the person asked to respond. Under war manners, direct questions and requests are permitted to save time and avoid confusion. (I suspect that in an emergency, war manners would supersede courtesy, e.g., "DUCK!" rather than "A wise person might choose to look up at this moment.")

At one point early in the story, the human protagonist tells the Elven queen something like, "I'm sorry, I'm just not very bright. I know you're getting at something, but I'm not going to understand unless you ask me." The queen then says something to the effect of, "Very well, but I would not have you think that you are being treated as a criminal."