Yes, in many fanfictions, Naruto is often depicted as a huge fan of the Fourth Hokage. After all, the Fourth Hokage is his father. Naruto grows up idolizing the Fourth Hokage's heroic deeds and wishes to be like him.
In this fanfiction, the plot might involve Naruto being tricked by an evil force into believing that the Fourth Hokage has some dark secrets. So he decides to fight him. It could also be a scenario where Naruto enters a different dimension where the Fourth Hokage is being controlled by an outside power, and Naruto has to free him by fighting. And during the fight, Naruto discovers new things about his father and his own abilities.
It could be that in this fanfiction, Naruto has been influenced by some false information about the Fourth Hokage. Some villains might have spread lies about the Fourth Hokage's actions, and Naruto, being young and naive in the story, believes those lies and thus starts to hate the Fourth Hokage.
The original Naruto story has a lot of themes about Naruto following in the Fourth Hokage's footsteps. However, in this fanfiction, with Naruto hating the Fourth Hokage, it goes against that theme and creates a whole new set of character motivations and plot directions. For example, Naruto might oppose things that the Fourth Hokage once stood for, which would be very different from the original where he tries to uphold the values of the village like the Fourth Hokage did.
One possible plot twist could be that Naruto has to face an unexpected enemy from the past of the Fourth Hokage. Maybe a hidden group that was against Minato's policies and now they see Naruto as a threat. Another could be that Naruto discovers a new jutsu that Minato was developing but never completed, which changes the power dynamics in the village.
It's really hard to say. The Fourth Hokage was incredibly powerful, with his Flying Thunder God Technique and all. But Naruto has the Nine - Tails' power and has grown a lot. If it was a fair fight, it might depend on who has the better strategy. The Fourth is more experienced in combat, but Naruto has that raw power. So it could go either way.
Another scenario could be during battles. Naruto might be inspired by the Fourth Hokage's battle strategies. He may think to himself, 'What would the Fourth Hokage do in this situation?' and then try to act accordingly. In some fanfictions, Naruto even visualizes the Fourth Hokage beside him, giving him advice during tough battles.
Well, it depends on the specific fanfiction. Some fanfictions might explore alternate storylines where Naruto doesn't become the Hokage at all. Maybe he decides to pursue a different path in life, like focusing on being a teacher or an explorer. However, in a large number of fanfictions, he does achieve his goal of becoming the Hokage because it's such an iconic and desired outcome for fans who want to see his journey to the top in different ways.
Perhaps Naruto feels that the Hokage has been too strict or unfair in dealing with certain situations. Like if the Hokage didn't support Naruto's way of trying to bring peace and unity, which Naruto firmly believes in. This could lead to a growing resentment and eventually hatred.
In fanfiction, Naruto's rule as the 5th Hokage might be full of positive changes. He would probably focus on improving relationships between the different ninja clans in the village. He'd also likely invest a lot in training the new generation of ninjas, using his own experiences to teach them about perseverance and the importance of friendship.