When you talk about atheism being involved in ethics you are going beyond atheism being merely the lack of belief in Gods which I believe is just a cover to retreat behind whenever nefarious antitheist subterfuge is exposed anyway.
Atheism has an indirect impact on ethics, as you need to explain the source of your particular view on any given moral point - religious people fall back on 'because God' (not meaning that dismissively, I appreciate there are scriptural citations to support a given point) whereas as atheism becomes more prevalent a moral philosophy has to be supported that does not rely on supernatural agencies for its foundation.
Finally, are the majority of children dyed in the wool atheists...rather than agnostic?
They are 'default' atheists - they have no concept of a god, and therefore no belief in one.
Again, to note, atheism and agnosticism are not differing positions on the same axis, they are perfectly compatible with each other, and are positions on two fundamentally different questions.
I'm not sure but atheists will have to watch that they don't fall into patterns of indoctrination.
People remain atheists by not falling prey to patterns on indoctrination. I'm not sure how you'd 'indoctrinate' someone into a position they are born into by default - if we don't mention gods, so children don't consider the idea, are we indoctrinating them? As it is, the best option is to introduce all the various concepts of divinity - at worst you'll get some sort of vague pantheist, and at best an atheist, but the chances of getting someone who picks one particular myth out of the bunch to cling to as 'truth' is diminished.
O.