Why can't we kick someone out of champion select? (People threatening to kill others in real life, etc.)
This would be extraordinarily easy to abuse (vote kick for not picking a desired champion, etc.) and allowing people to report in champion select would accomplish something similar without added abuse cases.
Why are we forced to play an hour with an AFK?
No idea, it's definitely frustrating.
Why do games continue at all with an AFK? (Games get paused in the LCS for the tiniest issues, but not for the paying community).
If games paused when someone AFKed, a pretty significant number of games would be constantly pausing and unpausing and being just as bad an experience as the AFK causes.
What is Riot doing to improve what is considered by most as the worst community in gaming?
Lots of things, it is just tough to make that impact particularly visible with the scope of the issue.
How can I still have people in my games threatening to kill my teammates and my parents?
They'll get banned eventually, it can just take time if the person isn't consistently that negative.
Why does Riot genuinely not care about the toxicity of League?
They do, there are multiple large-scale teams at Riot specifically dedicated to helping alleviate some of these problems.