It is not hard to run cheats for basically any game that uses video on another machine. Just a little more expensive (i.e. it is harder for someone in high school, but not anyone over 20).
Splitting the video stream to a second computer to run real-time video analysis and then send back commands through an emulated mouse may be doable, but it's certainly harder for anyone to do than copying chess moves on your phone.
Certainly! But it does show the amount of effort people will go to cheat - though lots of the "online shooter" cheating is people selling cheating tools/kits to idiots who want to win (basically turning games into pay to win).
The number of people who can build that kind of system from scratch is small.
I don't have details, but they're originally were designed for specific games - but the mechanisms can be adopted for others. The goal is to get a slight advantage on headshots, I believe.