One great Anakin Skywalker fanfic is 'The Fall and the Redemption'. It delves deep into Anakin's internal struggle between the light and dark side. Another is 'Anakin's Untold Journeys' which explores his relationships in a new light, especially with Obi - Wan. And 'Anakin: A Different Path' presents an alternate timeline for his character that is really interesting.
One idea could be a story where Anakin and Ahsoka are reunited after a long time apart. Maybe Anakin has been on a secret mission and Ahsoka has been exploring new parts of the galaxy. When they meet again, they have to work together to face a new threat that is endangering the Jedi Order.
There are some out there. However, the quality can vary greatly. Some might focus more on the romantic aspects between Anakin and the members of the harem, while others could be more action - packed with the harem aspect being a secondary plot. You really have to dig through different fanfic platforms to find the ones that suit your taste.
I really like the fanfic 'Anakin's Guidance for Rey'. In this story, Anakin, as a Force ghost, appears to Rey after she has started her Jedi training. He gives her advice on how to deal with the dark side of the Force, based on his own experiences. It has a lot of great dialogue and shows how Anakin has grown in his understanding of the Force even after his death.
One common theme is regret. Anakin often has many things he regrets in his life, like leaving the Jedi Order or harming those he loved. His crying in these fanfics can be a manifestation of that regret.
A common theme is the fall to the dark side. It explores how Anakin gradually becomes Dark Anakin, his internal struggles, and the events that lead to his transformation. Another theme is redemption. Some fanfics try to show a way for Dark Anakin to come back from the dark side.
A fanfiction could explore what would happen if Anakin Skywalker had survived and joined the Rebellion during the events of Star Wars Rebels. He would bring his incredible combat skills and Jedi powers. His relationship with other characters like Hera Syndulla and Sabine Wren would be interesting to develop, as they would have to learn to trust this once - fallen hero.
Well, it depends on the specific fanfic. Fanfic authors often take liberties with the existing lore. Maybe the author of that particular fanfic saw some similarities in powers or traits between Anakin and what they envisioned for Maka Rangnos' descendants and decided to make that connection. But it's not part of the mainstream Star Wars story.
A common theme is his struggle with destiny. In many fanfictions, young Anakin is constantly grappling with the idea that he's meant for great things, but he's also a normal boy from Tatooine. For example, he might be torn between wanting to explore the galaxy as a Jedi and missing his simple life at home.