It could be Gabriel Agreste. He has been a suspect in the original series for various reasons. He is often absent and has a lot of secrets. So in the fanfiction, it would make sense if he was finally revealed as Hawk Moth.
Common themes are transformation, not just in the sense of the Miraculous transformations but also in the characters' personalities. Hawk Moth might transform from a pure - evil figure to something more complex. Another is the exploration of the Miraculous powers. Fanfics often dig deeper into how the powers work and how they can be used in different ways against Hawk Moth. And secrecy is a big theme. Keeping identities secret, Hawk Moth's secrets, and how those secrets impact the story.
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.
One great fanfiction is 'The Hawk Moth's Redemption'. It explores an alternate universe where Hawk Moth starts to question his motives. Another interesting one is 'Ladybug and Hawk Moth's Unlikely Alliance' which has a unique plot of the two having to team up for a common cause. And 'Hawk Moth's Hidden Past' delves into his backstory and how he became the villain we know.
One possible plot could be that Ladybug and Chat Noir finally track down Hawk Moth's lair. They discover that Hawk Moth is someone they know in their daily lives, like a teacher or a neighbor. This revelation shocks them, but also gives them an edge in the fight as they now understand his motives better.
There's a fanfiction called 'The Miraculous Origins'. It delves deeper into the backstory of the Miraculous. It explores how the Miraculous were created and how they came to be in the hands of the current holders. It's a long read but worth it for fans who want to know more about the lore of the Miraculous Ladybug Cat Noir universe.
There could be fanfictions where Gabriel as Hawk Moth teams up with unlikely allies. Perhaps he realizes that his way of doing things is wrong and joins forces with Ladybug and Chat Noir to fight a greater evil that threatens the entire city or even the world.
I'm not sure of specific titles off the top of my head, but you can check out fanfiction websites like Archive of Our Own. There are likely many stories there that focus on Gabriel as Hawk Moth. You can look for ones with high ratings and lots of reviews.
In a fanfiction, Alix might get the Bunny Miraculous in a rather unexpected way. For instance, the Miraculous could be sent to her from an alternate future where she is the only hope. Once she has it, she struggles at first to understand the time - jumping abilities. But as she practices, she becomes a crucial asset in the fight against Hawk Moth. She could use the power to go back and prevent some of Hawk Moth's early akumatizations, changing the course of the battle.
Marinette and Adrien, as Ladybug and Cat Noir, finally decided to tie the knot. The city of Paris was filled with excitement. The wedding took place in a grand cathedral. Ladybug walked down the aisle in a beautiful white dress with red accents, while Cat Noir waited at the altar in his dashing black suit. Their kwamis were there too, Tikki and Plagg, looking on with pride. After the ceremony, they transformed briefly to soar over Paris as a newlywed superhero couple, sharing a kiss in the sky.