Most of these kids do not have mental illnesses. They may have mental disorders, which are different. Disorders can be treated to some extent, but they are more like an ingrained part of a person's psychology. A flaw that prevents them from fully integrating into society. You can't fully treat them or get rid of them. You can't cure mental illnesses either, as far as I'm aware, but they are much more uncommon. Few shooters had mental illnesses, but they likely were all disordered..
A distinction without much of a difference. Unless you told me all these kids had been studied and tested prior to or after the shootings for a diagnosis, your statements don't say too much. An "illness" is a clinical condition with severely debilitating and well-defined symptoms. A "disorder" is often nothing more than the "cocktail-of-the-week" high-functioning condition dreamed up and identified by someone as the new flavor upon which to base prescribing Ritalin or in justifying some aspect of behavior. Sheldon Cooper of The Big Bang Theory has a "disorder." But he doesn't walk into a school premeditated full of people he knows carrying a bag of guns planning to carry out a mass murder.
Disorders have been used often to justify and get people off as not being responsible for their crimes by crafty lawyers. I really don't give a flying crap what these kid's issues are, just that neither the parents, schools or their health administrators are apparently bothered to try to diagnose or detect it, and despite many calls to police and FBI by people who DID see the warning signs, the authorities apparently were loathe to deal with it.
Whatever the case, these kids are murderers, the public schools seem rather adept at cranking them out these days and it better be dealt with effectively pretty soon rather than trying to blame others and sit on their hands waiting for some white knight to come rescue them. These kids are killing people and must be dealt with in the most severe terms, and the schools and healthcare public authorities better get busy in coming up with a CAUSE, a treatment and an effective short term (school safety) and long term (better mental health) solutions. Frankly, from what I've seen of some teachers and school officials, public schools have been turned into loony, 24-7 government bureaucracies of endless and mindless rules and regulations and quite frankly, if I were a kid and had to put up with that shit all day long 5 days a week, I'd probably go off into deep end as well.
Time to get the government out of education and back into the private sector. It has been nothing but another federal total fail.