(a) What happens to B after B shoots A? What does B experience next?
B, like everything, reverses physical processes: the bullet flies out of A and back into the gun, and so on and so on.
What does B experience next? I have really no idea. But what we do know is that, in the story, only A remembers what happens. So I guess B, like, everyone else, doesn’t remember anything up until the restart — including the reversing (A doesn’t remember it either, for that matter).
(b) Does time just stop or cease to exist for B and everyone else like B, i.e., the rest of the human race and aliens (and trees, cats, dogs, the sun, etc. etc.)?
No, time continues on. There is just a period of time where physical processes reverse. If A spends a day before dying, then given the reverse takes as long as going forward, when A wakes up again, two days have actually passed. But the physical effects of those two days cancel each other out.
(c) Or does time go on? In that case, how does it go on?
It does go on. It goes on but without there being a noticeable change for anyone except A.
In that case, I can make sense of B killing A. The physical events to that point are leading to disaster. B literally reverses them back to the way they were at an earlier time. But what doesn’t happen is that anyone actually goes back to an earlier time. This isn’t time travel — it’s the appearance of time-travel.
Next (page 5 below): Conclusion (and some comments about actual time)