One idea could be that his dad initially reacts with shock and disbelief. He might start to question how he didn't notice all the signs before. Then he could try to use Adrien's identity as Chat Noir to further his own business or social standing in some way, creating a lot of internal conflict for Adrien.
Maybe a mysterious new character in the fanfiction. This character could be from Adrien's family's past, someone with a vendetta against his family, and decides to start by getting Adrien arrested to disrupt the family. For example, if Adrien's family wronged this character's family long ago, they see Adrien as a target to take revenge on the whole family.
It could be Ladybug. If Adrien turns villain, Ladybug would be the natural antagonist as she represents the good side. Their relationship would be completely flipped from what it was before. She would have to try to stop him from causing more harm, all while probably still having some feelings for the old Adrien.
These fanfictions usually show Adrien with a lot of flaws. He might be painted as being manipulative, using his charm to get what he wants without considering the feelings of those around him. Sometimes, he is shown as being irresponsible, not taking his role as a superhero seriously enough. They really dig into the idea that he is not as perfect as he seems in the original series. They may also show him as being overly jealous, which can cause problems in his relationships. For instance, if he is jealous of another character getting close to Ladybug, he might act out in a negative way.
Nathalie might be a character in these fanfictions too. Given her role in Adrien's life in the original series, she could be involved in the events leading up to his akumatization. Maybe she accidentally triggers his negative emotions. And then there's Gabriel, Adrien's father. His actions or lack of actions towards Adrien could be a major factor in Adrien getting akumatized. So, he could be a key character in the fanfiction, either as someone who realizes his mistake and tries to help or as someone who makes the situation worse.
Well, it depends on various factors. If the fanfic is appropriate and within the bounds of legality and good taste, it could be seen as a normal form of enjoying fan - created content related to a character or story he likes. However, if the fanfic involves inappropriate or unethical content, then it would not be normal or acceptable.
If Adrien were Hawkmoth in fanfic, it could change the dynamics of the story completely. It might explore his internal conflicts and the impact on his relationships with other characters.
He could also start acting out of character. Maybe he becomes more competitive towards Luka. If they are both in a band or something, Adrien might push himself harder to be better than Luka just to get Marinette's attention. He could also be more snappy or short - tempered with Luka, even if he doesn't mean to be.
Marinette is often a popular character. Since she has a relationship with Adrien in the original series, in the fanfiction, she could interact with the sister in various ways. Maybe they become friends, or there could be some initial jealousy from Marinette if she thinks the sister is getting too much of Adrien's attention.
Adrien could meet other mysterious figures in the lair. It could be an old acquaintance of his father's who has been helping with his secret plans. Or perhaps he'll come across a captive who was being held by his father for some unknown reason.