In this fanfiction, the plot could center around Anakin's struggle with the two different ideologies of the Jedi and Dooku. Dooku, as his trainer, might expose Anakin to the Sith ways. This could lead to Anakin having internal conflicts, as he has to decide whether to stay loyal to the Jedi or follow Dooku's path. His training could involve learning more aggressive and unorthodox Force abilities that are frowned upon by the Jedi, and his interactions with Dooku could gradually change his view of the galaxy and his place in it.
The main characters would surely be Anakin Skywalker and Count Dooku. Anakin is the protagonist in a sense as we would see his development through Dooku's training. Dooku, on the other hand, is the one who imparts his knowledge and skills, and his character would also be explored in terms of his motives for training Anakin.
One great 'anakin dooku fanfic' is 'The Duel Unseen'. It offers a unique perspective on their relationship and the events that could have happened between them.
Anakin managed to defeat Dooku through a combination of his raw Force power and determination. He used his lightsaber skills and quick thinking to gain the upper hand.
If Naruto was trained by Count Dooku in a fanfiction, Naruto would likely gain some very different skills. Dooku is a master of the dark side of the Force in the Star Wars universe, so Naruto might learn some unique combat techniques. However, his ninja way might be challenged as Dooku's teachings are quite different from what he's used to in the Naruto world.
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I'm not sure specifically as there could be many different takes in such a fanfic. But generally, it might involve Plagueis using his dark side knowledge and skills to train Anakin, perhaps leading Anakin down a different path in the Force compared to his canon training. Maybe Anakin would learn unique Force abilities or have a different view of the Sith and Jedi conflict.
Another plot could be that Anakin, without Jedi training, still has a connection to the Force but doesn't understand it. He might have strange dreams and premonitions that he tries to make sense of on his own. This could lead to him seeking out different kinds of mentors, not Jedi, but perhaps old hermits or wise women in the deserts of Tatooine who have a different perspective on the Force.
Anakin's mother, Shmi, would likely be a very important character. Since Anakin is not being trained as a Jedi, he would be more focused on his family. Shmi's influence on Anakin would be even greater, and she could play a role in guiding his actions and decisions, especially in relation to the local community on Tatooine.
The setting could be a major element. It might be set in a different time or place compared to the original Star Wars universe. Maybe it's during a period of relative peace, and the training is more about self - discovery for Anakin rather than combat - oriented. Also, the powers and abilities that the OC imparts to Anakin can be important. It could be new Force techniques or ways of thinking about the Force that we haven't seen before in the official stories.