So I've gone through the whole thing multiple times and have thrown out the garbage, added additional information here and there, consolidated and combined as much as possible wherever possible. I've also replaced all issue fixboxes with the support articles from the official knowledgebase where applicable (which was basically everywhere).
The Other Information section might still benefit from some time put into it here and there, and maybe I'll do so eventually. For example the "Change the language of a game" section could almost certainly be moved to a more appropriate section.
I am a bit uncertain about my change to the "Use Native Steam runtime mode" section (basically separated the existing info into an 'Advanced' subsection and added a new called 'Basic' with reference to Linux Steam Integration). If any Linux user could just check that it seems correct then I'd be grateful.