I am not too familiar with the AR platform, but perhaps there is some sort of funny business taking place in the throat area of your chamber. Specifically, the bullet could be engaging the rifling as it is seated in the chamber by the bolt, causing an interference fit between the rifling and the bullet. This would explain why the bullet remained lodged in your barrel upon extraction of the case, and would explain why the round that you thought had a bad primer extracted with an unseated bullet.
Now this doesn't explain the failure-to-fire problem, but that could be caused by excessive head-space. If there was excessive head-space and a particularly tight or shallow throat in your chamber these two factors together could cause this sort of behavior. As the bolt strips a round from the magazine and rams it home, the round's momentum may jam the bullet into the throat and then leave too much room between the bolt face and the primer, causing a light primer strike.
If you have any of the casings from the rounds that did fire, check them for bulging near the case head. This might not be as apparent with steel cases as it would brass though. Are there signs of engagement with the rifling or throat on the bullet?