I don't even own an AR; but in the first video, he keeps smacking the forward assist. Unless his rifle is extremely fouled, something is preventing the round from being chambered (read that: the rifle going fully into battery). Looks like an accident waiting to happen. In the second video, after blowing the magazine out of the magwell, I would stop and at the VERY LEAST field strip the thing. Probably have a smith look at it.
Some people strike the forward assist every time because they are trained that way, or saw it in a movie once. Its not hard to get a feel for a forward assist strike that does nothing, versus hearing that click of the BCG going into battery. Every time I hit the forward assist and it actually does something, I investigate why it didn't go into battery the first time. Its usually user error, like a sling interfering with cocking handle, etc. I've seen fouling be the issue with some people, but it has to be pretty filthy, or neglected for that to be the cause.
As for the second vid, You can hear that no round gets picked up from the second mag when he cocks it. That should be an indicater. We also then see the new mag fall out. I'm curious if that's because of simple user error and not making sure the mag was properly seated, or if because the frame of the rifle was deformed and magazine catch was no longer able to reach the magazine properly. After something exploded, I definitely would have called it a day right there, and gone back to the lab.
I've only been reloading for about 3 years, and have only made about 5,000 rds or so. Never had a FTF. Two in a row? Definitely would have stopped there to investigate. I'm especially curious about the relationship between FTFs, Magazines exploding, and bullets lodged in the barrel.
I suspect overheating causes the first two, with the 3rd being somewhat unrelated, other than the user failing to notice.