12.How did Uncle Chuck create Power Rings, and why did he make them for Sonic before the whole Coupe?
The rings have always been associated with the power of the Chaos Emeralds; being the leftover residue of their radiation. I'm not so sure how Uncle Chuck created them, but the series did suggest them being used as energy sources and amplifiers.
Perhaps that's where the Archie comics got the idea.
The glowing solid in the device producing power rings could have been a specific type of rock which stored some of the chaos potential energy after being exposed to a chaos emerald for a long period of time in the ground. Mobotropolis likely did not have access to chaos emeralds, but they utilised the energised gangue for energy.
Chuck could have designed the device, which captures the chaos energy from the gangue and stores it in manageable amounts within rings which release it in the presence of consumers of the energy, such as appliances, transducers or specific mobians.
During the coupe, Sonic was five years old (as far as I remember correctly), so Chuck probably did not intend for Sonic to use them in combat. Perhaps they were not intended for Sonic at all in the first place. He could have come upon them by chance, discovered that he could enhance his superspeed with them, so Chuck manufactured some for him.
4.What Happened to Cat, Robotized, Killed, or other?
I would assume he was Roboticized, given that's what happened to Ari's group.
Which reminds me of the bear and the equid in Blast to the Past part 1, who were captured and roboticised after their sabotage. Based on the fact that the Freedom Fighters were surprised about how promptly they were roboticised, there would most likely be no time for interrogation. Robotnik or Snively must have known that they were associated with the Freedom Fighters of Knothole, because Sonic was detected.
So why weren't they interrogated and Cat was?