Yes, there might be such fanfictions out there in the vast world of fan - created content. However, this goes against the general storyline of the Naruto series where they are comrades.
It's a rather unique concept. In the original Naruto series, Kakashi is a mentor figure to Naruto. The idea of Kakashi killing Naruto goes against the general bond and narrative. So in fanfiction, it's not a common theme as most fanfics tend to follow the positive relationships from the original. However, it can attract those who like exploring dark or alternative storylines.
The other villages might react with a mix of shock and suspicion. They knew Naruto was a powerful force for good in the ninja world. His death could be seen as a sign that something was amiss in Konoha. Some villages might even fear that Konoha was becoming unstable and could pose a threat. Characters like Gaara, who had a special bond with Naruto, would be deeply saddened and might try to find out the real reason behind Naruto's death.
One possible plot could be a dark turn in the story. Maybe Kakashi is under some kind of mind - control. He could be forced to fight Naruto by a powerful enemy who has taken over his mind. Naruto, being unprepared for such an attack from his mentor, gets killed. This would then lead to a series of events like Sasuke going on a rampage to find out the truth and avenge Naruto, and the whole ninja world being in shock as one of their most promising heroes is gone.
The villagers of Konoha would be divided. Some would trust Kakashi and believe there was a good reason for Naruto's death, while others would be furious. The older generation, like Tsunade if she was still around, would demand an investigation. And for Hinata, she would be the most affected. She might feel like she lost her purpose in life with Naruto gone, but then find new strength in seeking justice for him.
One possible plot could be that there is some sort of misunderstanding or dark magic at play. Maybe Kakashi is being controlled against his will. In the 'Naruhina' aspect, Hinata could be devastated by Naruto's death. She might initially suspect foul play within the village and start her own investigation, all while struggling with her grief and her unfulfilled love for Naruto.
Well, there could be. Fanfiction writers love to explore unique and unexpected relationships. Since Naruto and Kakashi are both popular characters in the Naruto universe, some writers might come up with such a plot for the sake of creativity and exploring different storylines. But it's not a part of the official Naruto story.
Sasuke could be a popular character. He might be involved in the story in a way that either helps or hinders the situation where Naruto hurts Kakashi. For example, if Sasuke tries to stop Naruto from doing something stupid that would hurt Kakashi.
Another reason could be related to Kakashi's past actions. If there are some secrets or things Kakashi did in the past that come to light and Naruto doesn't like them, he could snap at Kakashi. Naruto has a strong sense of justice and loyalty, so if he feels betrayed or misled by Kakashi, his reaction could be to snap.
Kakashi might be initially surprised. But then, he would probably use it as a teaching moment for Naruto. He could say something like 'Naruto, stealing is not the way of a ninja.' And then give him a punishment like extra training.