I generally suck with looking at photos, but some of those do look over pressure, but I have seen worse. The best looking one to me is top row second from the left, all the others are.....ehh too much for me.
Rifle should be ok, the primer is fairly soft, and even if it gets stuck in the innerds of the rifle, I highly doubt real damage will be done.
What would (I) do?
Not shoot any more of those, and if I have boxes from that same lot I would not shoot them as well. Get on the horn to the maker and say ahh hay I think we have an issue here.
The primer should not leave the case unless you are reloading and poking it out. To leave the case only a couple things, too much pressure, or the pocket (where the primer goes) is too big, it generally happens on well used cases like the other poster said.
If this is a bolt rifle, and they are a tick too long it will not want to chamber, if an auto same basic thing, the thing will not want to close. If everything "feels" fine it likely is not too long and hitting the "rifling". You could also measure and see how long they are.
The "carbon ring" seems to be the new word on gun forums lately, a little like when you have a 3yr old and he learns a new word it is all so many can talk about. I have shot a very long time, and don't clean very often, never had the issue. That does not mean it is not something that could happen, all I am saying is I have never seen it happen.