You can also get punched-out primers from having a primer cup which is too hard to start with; at one time there was a LOT of that going around.
Primer on the far right looks to be flattened excessively, possibly oversize: pressure or headspace or both, depending on the actual diameter of the primer.
People demand performance, so the factories load their ammo absolutely "to the nuts" in order to get the final ounce of performance from every round. There are some makes of ammunition out there which carry this much too far; I started having primer punch-outs and blow-outs and hard extractions with a certain brand of European ammo in 6.5x55. There was absolutely nothing wrong with the rifle, but the cases were exhibiting the same problems as yours. In the end, I put a couple of the rounds aside in the 'general collection' tub and pulled the rest of the box down and reloaded it with a load which I KNEW was safe. No more problems.
The Italians generally were pretty careful with headspacing their rifles. It is much more common to find rifles with bolts on the TIGHT side than it is to find them with bolts on the loose side. Cooey also was careful in rebuilding these rifles (they started with Fucile 91s).
If it were my ammo and my rifle, I think I would be inclined to pull down the remaining ammo and reload it with a charge you KNOW is not excessive, replacing the primers at the same time.
Question: when you chamber a round and lock the bolt down, is there any resistance from the bolt? If it is tight at that point, the problem is NOT the rifle.
To test if the ammo is okay, you should be able to load in a round from the magazine, lock the bolt, unlock the bolt and CHECK to be sure that the Extractor is HOLDING the cartridge to the face of the Bolt. Then you turn the rifle away from you and fire that one round from the hip. Open up the rifle and check the casing. Same problems? If so, it's the ammo for certain.
BTW, any Carcano should be loaded through the Magazine, same as any other Mauser variant. Tossing a round into the chamber and slamming the bolt shut runs an awful risk of damage to the extractor. There were 3 types of extractors..... and 2 of them are turkey-teeth. I DO hope you are using a Clip to load your rifle.
Good luck, friend.
Hope this helps.