Well, it depends on how much his dad knows about Cat Noir. If he doesn't know much, he might be a bit confused at first. He could ask Adrien what exactly a Cat Noir fanfic is all about. Maybe he'll be dismissive if he thinks it's just some silly fictional thing that distracts Adrien from more 'important' matters. But on the other hand, if he realizes it makes Adrien happy, he might be more accepting in the long run.
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.
There is a possibility that it could lead to a better understanding between them. Adrien showing his interest in the Cat Noir fanfic could be a way for his dad to see a different side of him. If his dad is open - minded enough, he might start to respect Adrien's individuality more and this could improve their relationship overall.
In some fanfictions, Cat Noir's reaction is more complex. He is excited to know but also realizes the great responsibility that comes with this knowledge. He becomes extremely protective of Ladybug's identity. He might start to distance himself a bit in order to not accidentally give away her secret. At the same time, he has to deal with his own feelings for her which are now even more intense since he knows who she really is.
On the other hand, it could bring them closer. His dad might start to see Adrien in a new light, as a brave and capable hero. This newfound respect could lead to a more open and trusting relationship between them.
No. In the normal 'Miraculous' series, Cat Noir is a superhero, not a criminal. Fanfiction might deviate from the original, but the general perception of his character is heroic. So, just because it's a fanfiction doesn't mean he's a criminal.
Obviously, their best friends like Alya and Nino would be there. Alya could be Ladybug's maid of honor, and Nino could be Cat Noir's best man. Also, all the other superheroes they've worked with in Paris would be invited. And of course, their families, if their identities were revealed by then. Maybe even some of the citizens of Paris who have been saved by them over the years would show up to celebrate this special occasion.
Well, in some fanfictions, Hawkmoth might use false promises. He could promise Cat Noir something like the power to save a loved one in exchange for his help.
One great 'Cat Noir and Ladybug Fanfic' is 'The Miraculous Bond'. It delves deep into the relationship between Cat Noir and Ladybug outside of their superhero duties. It shows their normal lives and how they gradually realize their feelings for each other in a very sweet and believable way.