Sounds like a long tedious elimination process is ahead. But since the only errors you get regard KDE, I’d try installing another desktop environment. Afterwards you can generally choose which desktop to log into at the login screen. And when it’s resolved whether or not KDE is the problem, you can easily switch back if you want. So it’s very easy to try. But each elimination will take 5 days!! If the computer behaves the same each time it crashes, it is definitely NOT random. If it was random it would be different things each time, and then it could be RAM or even CPU problems. But this sounds like a software problem.