Regarding the percentage of guns that are used in violent crimes that were obtained by private sale, at a gun show or otherwise, without a background check, I have tried to obtain better statistics on this. The people who think it's a significant percentage include:
Center for Crime Prevention and Control at John Jay College of Criminal Justice in New York
Violence Prevention Research Program at the University of California-Davis Health System
Fordham University Law Department
And of course several law enforcement agencies. Unfortunately, and I write this to be as honest as possible, despite the assurance from all of these sources that the number is indeed significant, none provide any studies or statistics to back it up (at least that I can find.)
Meanwhile the NRA, Heritage Foundation, and CATO Institute, all of which oppose universal background checks, all rely on the 1997 Justice Department study that Oogie Pringle quoted.
Based on all of this information, my answer to Rayderr is: I don't know; I suspect that it's higher than you think it is, but there's no way to tell until a few years after we impose universal background checks, of which I continue to be in favor of.