Ammo can cause both of your problems and sometimes a failure to eject can look like a double feed. This can also be caused by ammunition that is both under-powered and over-powered, and I've seen it happen both ways. I'm inclined to say that since the gun is having two problems at once, it is not the magazine.
When I went to the police academy, we were all issued Bushmaster carbines. Almost immediately a significant portion of us began having both extraction problems and what appeared to be double feeds. Since the academy was a semi-military environment, when someones rifle had a jam, it was that persons job to immediately clear it and keep shooting. Since the guns were almost new but the magazines (D&H) were hand-me-downs, a bunch of people rushed out to Academy sports and bought themselves P-mags to solve the problem.
The thing was though, the new magazines didn't solve any problems and even the instructors noticed this. When someone next to me had another double feed, I stopped him from clearing the jam and watched him as he did. When he locked the bolt to the rear, out came both a new round and an expended round. From the outside it looked like a double feed because two cartridges were trying to force their way into the chamber at the same time. But what had happened was the extractor couldn't hold on to the fired casing. Without the extractor holding on, the ejector couldn't swing the casing out. Pressure from the barrel pushed the casing back with the bolt, the bolt picked up a new round from the magazine, and then both casing were pushed forward into the chamber.
When we took apart our bolts, we saw that Bushmaster had used a blue rifle insert and what I assume to be an under-powered extractor spring. Once they were replaced with a black insert and a 5-coil spring, all problems went away.
From your description of the problems, and how they went away with a different choice in ammo (which it won't do if the magazine is truly giving double feeds), he needs to upgrade his extractor spring and insert, possibly the extractor, or just replace the bolt.