I don't have enough time to go into detail about your questions so I will give you a quick opinion. However I recommend you used the Search bar for this site. All of the questions you asked have been answered before and you should have no problem finding them in the archives.
Basically it comes down to shot placement. Can a .22 stop someone if you shoot them in the head? Sure. Will a .22 stop someone if you shoot them in the foot? Doubt it. Will a .45 stop someone if you shoot them in the head? Sure. Will a .45 stop someone if you shoot them in the foot? Might slow them down but won't kill them. I think you get the point. A 500 S&W Magnum is not going to kill someone if you miss them. Carry as big of a gun as you are accurate and quick with. A .22 would offer a lot quicker follow up shots but not nearly as much energy and lead as a .45.
I choose the 9mm round. I am most accurate with it for a few reasons. I am able to handle the recoil better and therefor hit the target more often, I am able to make a follow up shot faster because of the manageable(to me) recoil, and most importantly I am able to do these things because I can afford to practice often with this round and become competent. Plus I feel that a good quality 9mm hollow point offers enough "stopping power".