A 'Naruto modeled after Kakashi' fanfiction could see Naruto with a changed appearance to some extent. He might start wearing his headband in a similar way to Kakashi, or even have a similar style of clothing. In terms of his ninja skills, he could master the Sharingan - like abilities in some form, perhaps a new jutsu inspired by it. His mentoring style could also change, becoming more like Kakashi's, being tough but fair with his students or comrades.
Yes, there are some. However, the popularity can vary. Some are popular within certain fan communities. You can usually find them on fanfiction - specific websites by using relevant search terms like 'Naruto modeled after Kakashi' or something similar.
His relationship with Sasuke would be completely different. Instead of being rivals, Sasuke might see Naruto as a sort of replacement for Itachi, which could lead to a very complex dynamic. Maybe Sasuke would be drawn to Naruto in a strange way, not sure if he should hate or befriend him.
It would be really strange. Naruto is much younger than Kakashi in the original story. But if it were a fanfiction, maybe it could involve some time - travel or alternate universe concept. Naruto could use his experiences to raise Kakashi in a different way than Sakumo did.
One reason could be for guidance. Naruto often looks up to Kakashi and might need his advice on a difficult situation, like dealing with a new powerful enemy.
One possible plot twist could be that Naruto, while modeled after Itachi, has to face off against Sasuke who mistakes him for Itachi at first. This would create a really tense and emotional situation as Sasuke's hatred for Itachi might be misdirected towards Naruto.
In such a fanfiction, Naruto might adopt Kakashi's laid - back attitude. He could start reading those 'adult' books Kakashi likes in his free time, and also become more of a lone wolf in his missions, relying more on his own skills like Kakashi does.
It would be a relationship full of growth. Kakashi would be a father figure to Naruto. He would encourage Naruto to study and learn from his mistakes. Given Kakashi's love for reading, he might introduce Naruto to different books and philosophies that would help Naruto in his ninja career. Naruto, in turn, would bring out the more emotional and caring side of Kakashi that he usually hides.
In such a fanfiction, Naruto might become more strategic from an early age. Kakashi's intelligent and cautious fighting style could influence Naruto. He might teach Naruto more about the Sharingan he got from Obito earlier, which could make Naruto's combat skills more diverse.
If Naruto was adopted by Kakashi and Anko in fanfiction, the story would take an interesting turn. Naruto's development would be affected in multiple ways. Firstly, in terms of his training, he would have access to a wider range of knowledge. Kakashi is known for his vast array of jutsu knowledge, and Anko has her own set of skills. This would make Naruto a more versatile shinobi. Secondly, his emotional growth would be different. Growing up with Kakashi and Anko, he would experience a more loving and nurturing environment. They would be able to guide him through his insecurities and help him better understand his power as a jinchuriki. Moreover, the story could also explore how Naruto's new family situation would impact the village politics and his relationships with other clans and ninja. For instance, the relationship between the Uzumaki clan (to which Naruto belongs) and the Hatake and Mitarashi clans (Kakashi and Anko's respectively) could be developed further, creating new alliances and storylines within the fanfiction.
Their relationship could be one of mentorship from the start. Kakashi, with his skills and knowledge, could start teaching baby Naruto simple ninja concepts early on. He would also be very patient with Naruto, understanding that he's just a child and has a lot to learn.