Satan is a rather interesting character who seems to have two sides: the evil and violent side that punishes others by damning them to hell, and a soft and compassionate side that we see when he's in a romantic relationship, or when he wants to help educate others.
In earlier episodes, Satan seems to only be interested in taking over the world and otherwise causing misery for others. He tries to take over the world twice in the series, and he challenges Jesus to a boxing match,with most of the people watching betting on Satan due to his immense size and strength, only to throw the match and reveal that he himself bet on Jesus winning, therefore taking everyone's money.
Satan is actually homosexual and is on and off in several relationships with other men throughout the series, most notably Saddam Hussein. Matt Stone and Trey Parker, the creators of South Park, took inspiration from mock interactions between the characters that they enacted. Saddam is emotionally abusive to Satan and only used him for sex and to help him in taking over the world himself. Satan eventually kills Saddam by throwing him back into Hell, where he was impaled.
Satan occasionally offers advice, usually to Stan, He teaches Stan about the pricing structure that fee mobile games use, before possessing him in order to travel to Canada to defeat the Canadian Devil, who was profiting off of one of these games.
https://en.wikipedia.org/wiki/List_of_recurring_South_Park_characters#Satan
https://www.youtube.com/watch?v=B29YStCYorY
https://www.youtube.com/watch?v=Qzw00i4JExw
