It could strengthen Naruto's relationship with Iruka. Since Naruto is the son of the fourth hokage, Iruka might see Naruto as an even more important part of the village and be even more protective. For example, he could be more involved in Naruto's advanced training.
Kushina is an obvious choice. In fanfictions, they can have more adventures together, or their relationship can be explored in more depth. Their love story is already quite popular in the Naruto series, and in fanfictions, it can be expanded upon, like showing more of their courtship days.
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.
One interesting plot twist could be that the fourth hokage didn't actually die when he sealed the nine - tails in Naruto. Instead, he was trapped in a sort of limbo within Naruto's mind and could communicate with him at crucial moments, guiding him in ways that no one else could understand.
One option is a new, original villain created just for this fanfiction. This villain could be someone who wants to rewrite history and prevent the Fourth Hokage from ever becoming Hokage. So they target Naruto as he is the son of the Fourth Hokage. They might have some sort of time - traveling or reality - warping powers.
Naruto himself is often a popular character in these fanfictions. Since he is the main character of the original series and has a connection to the Fourth Hokage as his father, his presence adds depth to the story. Kakashi is also common. His relationship with the Fourth Hokage was that of a student - teacher, and it can be further explored in fanfictions.
In most official Naruto lore, Naruto is not related to the Second Hokage. However, in fanfiction, anything can be possible. Some fanfic authors might create a story where Naruto is the Second Hokage's son for the sake of creating a unique plot twist or exploring different character relationships.
One interesting Naruto Fourth Hokage fanfiction could be one where he survives the fight against the Nine - Tails. In this kind of fanfiction, he gets to see Naruto grow up and train him personally. It would be a heartwarming story of a father - son relationship that was cut short in the original series.
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.
In this fanfiction, Naruto might finally get the fatherly guidance he always craved from the Fourth Hokage. Maybe the Fourth Hokage would teach Naruto some long - lost jutsu that only he knew. It could also be a chance for Naruto to understand his father's sacrifices on a deeper level.