I don't have a model which I believe with certainty even provided MWI is true.

I think that, given MWI, your consciousness is in any world in which you exist, so that if you kill yourself in the other worlds, you only exist in worlds that you didn't kill yourself. I'm not sure what else could happen; obviously you can't exist in the worlds you're dead in.

What happens if you die in a non-MWI world? Pretty much the same for the case of MWI with random branch choice. If your random branch happens to be a bad one, you cease to exist, and maybe some of your clones in other branches are still alive.

So at time t, the data is already determined from the computer's perspective, but not from mine. At t+dt, the data is determined from my perspective, as I've awoken. In the time between t and t+dt, it's meaningless to ask what "branch" I'm in; there's no test I can do to determine that in theory, as I only awaken if I'm in the data=n branch. It's meaningful to other people, but not to me. I don't see anywhere that requires non-local laws in this scenario.

Non-locality is required if you claim that you (that copy of you which has your consciousness) will always wake up. Otherwise, it's just a twisted version of a Russian roulette and has nothing to do with quants.

At time t, the computer either shoots you, or not. At time t + dt, its bullet kills you (or not). So you say that at time t you will go to the branch where the computer doesn't kill you. But such a choice of a branch requires information at time t + dt (whether you are alive or not in that branch). So, physical laws have to perform a look-ahead in time to decide in which Everett branch they should put your consciousness.

Now, imagine that your (quantum) computer generates a random number n from the Poisson distribution. Then, it will kill you after n days. Now n = ... what? Well, thanks to thermodynamics, your (and computer's) lifespan is limited, so hopefully it will be a finite number -- but, look, if the universe allowed unbounded lifespan, it would be a logical contradiction in physical laws. Anyway, you see that the look-ahead in time required after the random number generation can be arbitrarily large. That's what I mean by non-locality here.