Here are my suggestions on securing your coop and run. i don't see a latch on the egg door on the coop. You should put on at least one, if not several. Your run looks to be made with chicken wire, which won't stop a predator, as it is easy to chew through. Ideally you will want 1/2" hardware cloth. The door looks to have gaps at the top and bottom. A weasel or other small predator might be able to get in easily. Luckily we don't have weasels where we live, but i have heard they can get into very small spaces, like a 3" opening. Plus, you really want a latch on the top and bottom of that door, too. Looks like it would be easy to pull the door open at either end.
You probably do have feather picking due to the confined quarters. But i've never heard of chickens disemboweling each other. That sounds like a predator. Not an expert on that, so others can help more on what kind. Also, having a light on all the time probably keeps them from getting adequate sleep and can contribute to antisocial behavior.
i'm very sorry for what you're going through. i hope you can find out what is doing this.