Disclaimer, I had horses in my youth, however I am not an adult horse person.

The answer to a lot of your questions is that a reasonably well trained (and well tempered) horse should let most anyone ride it. Horses are pretty smart and can definitely get some anxiety if someone completely new just shows up and tries to ride them, but again, if they are well trained they know that they have a job to do and they do it.

I can’t speak specifically about if a horse watched its owner die how it would react, so I’ll lean into your western scenario. If someone walked up to me and shot me with a gun in front of my horse, and my horse was not familiar with gun shots, then the horse would probably get spooked and run away. Horses are flight animals and once they’re spooked every instinct they have tells them to run.

As for telling at a glance how “obedient” a horse is, I can only say that I personally am not so skilled with horses that I could tell that. I can get a read on a horse’s current mood based on how it reacts to me, but that involves interacting with the horse a bit and I can’t say I’m perfect at it. Every horse has a different personality, similar to people.

Hope that at least gives you some answers!