Guns sold by dealers with FFL requiring background check- DONE. Guns sold privately, no check. Will ALL private sellers do a background check? Not a flippin' chance. They'll just buy and sell guns "off the books", just like they do now.

I'm all for people being trained- far less chance of hitting an innocent bystander but the problem remains- criminals WILL get guns.

You're completely ignoring the fact that this is a behavioral problem. If people could deal with conflicts without resorting to violence, most of this would never happen.