In Germany, if 14-18yolds make nude selfies then nothing happens, if they share it with their intimate partner(s) then neither, if someone distributes (that's the key word) the pictures on the schoolyard then the law is getting involved. Under 14yolds technically works out similar just that the criminal law won't get involved because under 14yolds can't commit crimes, that's all child protective services jurisdiction which will intervene as necessary. The general advise to kids given by schools is "just don't, it's not worth the possible headache". It's a bullet point in biology (sex ed) and/or social studies (media competency), you'd have to dig into state curricula.
Not sure where that "majority of cases" thing comes from. It might very well be true because when nudes leak on the schoolyard you suddenly have a whole school's worth of suspects many of which (people who deleted) will not be followed up on and another significant portion (didn't send on) might have to write an essay in exchange for terminating proceedings. Yet another reason why you should never rely on police statistics. Ten people in an elevator, one farts, ten suspects.
We do have a general criminal register but it's not public. Employers generally are not allowed to demand certificates of good conduct unless there's very good reason (say, kindergarten teachers) and your neighbours definitely can't.
We actually did. Trouble being you need experts to feed and update the thing, which works when you're watching dams (that doesn't need to be updated) but fails in e.g. medicine. But during the brief time where those systems were up to date they did some astonishing stuff, they were plugged into the diagnosis loop and would suggest additional tests to doctors, countering organisational blindness. Law is an even more complex matter though because applying it requires an unbounded amount of real-world and not just expert knowledge, so forget it.