But consider this in conjunction to your statement: The only reason Satan punishes bad people is because he's wanting to get back up to Heaven because he's learned his lesson and is a good guy again

no he DOES NOT punish bad people, he is stuck in hell being punished with the bad people he has no authority in hell he is just another damned soul

Ah, but if he is no better than the next man there for eternity, why is he made out to be the one in charge? A sort of Alpha-Demon if you will

thats a misconception that started in "paradise lost" when satan said "better to regin in hell then to serve in heaven" many people are dumb and believed this to be true rather then read the bible which states that satan gathered some angels and started a rebellion in heaven which was quickly stop and God cast satan along with all the angels that took his side where cast to hell. you can call him alpha demon in the way he lead the rebellion, however his punishment in hell is that same as anyone else in hell

Revelation 12:7 says "And there was war in heaven. Michael and his angels fought against the dragon, and the dragon and his angels fought back." the dragon being satan suggesting he had angels on his side

On his side? Or enslaved by the silver tongue that manipulated Eve?

im not entirely sure on that one but i believe it was angels he convinced to join his side