The second time happened to me recently shooting my son's Springfield M-1A. I had what is referred to as a slam fire. You shoot the first round and when the bolt cycles, it sets off the newly chambered round. As usual, I had complete control of the rifle and both shots actually hit the target about 8 inches apart. I know what causes it but I'm not quite sure why it happens. This was in a new rifle, not some worn out piece of junk.
It's probably more common in new rifles. Remove the bolt and make sure there is no lubricant of any kind in the firing pin hole! The firing pin should rattle forward and back freely when you shake the bolt.
The two most common causes of rifle slamfires I know of are both in rifles with floating firing pins; primers that are too soft or a sticking firing pin, usually from grease in the firing pin channel.
Make sure that no grease or oil goes on that firing pin.
About the closest thing I've come to an ND was when my father's Saiga bump-fired on the bench at our range. I had my suspicious that it was a bump-fire but the rifle got unloaded and checked over for any mechanical defects.
Probably hammer follow. Not too uncommon in AKs, but fairly easy to fix usually.