Even if he cheats, he won't find anything here.

How and why is there a connection between a player adding someone to their personal blacklist and the player's rating?

There isn't any. These are two different ratings.
One is the main rating, which depends on the number of wins/losses and the strength of the opponents. It doesn't go below 0.
The other depends on the number of people who enjoyed playing with you (they add you as a friend) or with whom you no longer want to play for various reasons (toxic players, unstable players, quitters, noobs) (adding to the blacklist).
There are players with a rating of -40; naturally, it doesn't make sense to start a game with them; it's a waste of time.
The same applies to the Soda Lobby.