The offenses described are not offenses, if for which he is convicted, would prevent him from owning a gun. Failure to appear, contempt of court, etc, are actually more harmful. It asks on the 4473 if you are a fugitive from justice. Technically, right now he is.
I left the country for two years, came home, and bought a gun two days later. Background check, took it home, no problem. Two weeks later, I got pulled over for a bad taillight, and I popped for a warrant, failure to appear, suspended license. I was in the city lockup for three hours before they were able to decide that it was likely an error due to poor recordkeeping on the part of my former insurance company, my VERY common first and last name, and not worth holding me for, since in all likelihood I would make a couple of phone calls first thing in the morning and straighten it out, (Which I did.) The point is, none of that stuff was in the system after two years. Petty civil stuff, maybe it will go in, maybe it won't. Who knows. My experience is that city courts can be VERY um, overworked and behind in their processes, which often results in all kinds of errors. (I have also used this inefficiency to get out of a couple of tickets.)
The bad news is, if your friend's city is much better organized than mine, he will go to make the purchase, and either be refused, have the refusal remain as a mark in the system, or worst of all, the guy selling him the gun is the sheriff's brother in law, and he will stall him long enough to show up, cuff him, toss him in the city joint until he chokes it up. Does he feel lucky?