Would it make sense to provide a place for a subgroup or two where young people can ask and answer questions appropriate for their level of education? Say ElementaryMath and HighSchoolMath? Then perhaps give a day for people within the group to answer after which any of us could answer.
Poor fit for SE
Setting aside the highly discriminatory idea that age is a suitable grouping metric for learning, there are several problems with your suggestion.
If you want such a site, I suggest you propose one on Area 51 and rally people to support the proposal. However, your proposal has several problems that make it a poor fit for an SE site. I, for one, would not be active on that site, for the reasons I give below.
The purpose of StackExchange is to create a repository of high-quality questions and answers. We are creating a reference book, not replacing a tutoring center. In a comment, you say:
Content in A and B levels could be purged on a schedule. We don't produce pre-programmed young people. The new generations have to repeat what we've done.
This idea of purging questions and answers periodically is antithetical to the purpose of StackExchange.
However, even if your idea was in-line with SE goals, implementing a "subforum"-like structure with separate permissions depending on age would be a large change to the SE engine. We are not the only site that uses the SE engine, so any such change would have significant effects for the other 132 sites on the network.
Finally, you suggest allowing children under $13$ to post questions/answers. This is not in-line with the SE terms of service, for reasons outlined here.
Over the years, I've seen several suggestions on Meta.Math.SE that are borderline site-overhauls. (I consider this suggestion to be one of them.) These suggestions are nearly always made by relatively new users. That makes me feel uneasy, as it is similar to the person who walks up to a group of people having a nice conversation and hijacks it to talk about something else.
Don't get me wrong--I'm all for improvement. But, many of these "overhaul suggestions" would be better suited as ideas for new websites not related to StackExchange.
Fundamentally, I disagree with any suggestion that seriously restricts who can answer a question. A simple question may benefit from a sophisticated answer. I think my greatest contributions (which is closely approximated by my highest upvoted posts) to the site are very accessible to anyone and are substantial answers to simple questions, and I most appreciate these contributions of other people as well. Experience, in both mathematics and mathematical writing, aids the creation of such posts. It is thus desirable that we should have experts (in whatever sense you want to take this) answering good but "easy" questions and additionally that, when the stars align and an awesome question/answer pair shows up, we should keep it forever. Any restriction on question answering will get in the way of this process - even a delay would make experts less likely to browse questions.
Aside from the intrinsic problems with the idea, it's also unclear how one would implement such a feature. How do we decide what "level" a question is at? Question askers certainly aren't good judges of how hard a question is, and given that algebra-precalculus questions are so often tagged as abstract-algebra, we can't exactly go off of tags. And who, in the first place, is going to decide exactly how the graduations are set up?
It sounds like you're proposing a different site than what SE intends to be. This site is really good at getting questions answered well - that's what's it's set up to do. As someone who primarily answers things, I can I learn a whole lot while I answer questions - but this isn't more of a byproduct which only needs to exist insofar as the site needs to attract answerers (which it seems to be doing). The primary goal is that this site will be a high quality collection of questions with useful answers. Your idea is not, in some universal sense, bad, but it does not fit here.