Lucifer and Satan were not the same person. Although Lucifer was called the Morning Star, it did not explicitly indicate that he was Satan. Satan was the name of the ancient snake, and Lucifer was an independent existence. Therefore, Lucifer Morgenstern was not Satan.
I don't think Darren Modok was featured in the comics. Usually, characters like this don't just pop up without notice or a lot of buzz among comic fans.
One common theme is self - discovery. Since Clary has a complex character, many fanfics explore how she further discovers herself. Another theme is love and relationships, whether it's her relationship with Jace or other characters in the story.
One common theme is redemption. Since Valentine Morgenstern is often a complex and somewhat villainous character, many crossovers explore his journey towards redemption when placed in new situations with different characters. Another theme is power struggle. When combined with characters from other universes, there's often a battle for power or influence.