No. In the original Naruto series, Naruto is the son of the fourth Hokage, Minato Namikaze. Fanfics may create alternate universes, but the canonical relationship is that Naruto has no relation to the second Hokage in the official story.
Well, the whole story would be very different. Naruto might inherit different jutsu from the second Hokage instead of the fourth. His relationship with characters like Sasuke and Sakura would also be re - imagined. Maybe he would be more proficient in water - based jutsu.
Obviously, the Second Hokage himself should be a main character. His brother, the First Hokage, could also be included, perhaps in flashbacks. Then there could be some of his students, like Hiruzen Sarutobi. The Uchiha clan members might be important characters too, since they play a significant role in the village's history and the Second Hokage had interactions with them.
Sasuke could also be a possibility for the 6th Hokage in the fanfic. He has grown stronger over the years and his unique perspective on the ninja world could bring new ideas to the leadership of the Hidden Leaf. He might start off as a controversial choice but prove himself through his actions in protecting the village and making tough decisions.
Yes, there are likely many fanfics with that theme. The Naruto fandom is huge and creative, so it's common to find fan - made stories exploring different 'what - if' scenarios, like Naruto becoming the fifth Hokage. You can look for them on popular fanfic websites.
A really interesting plot could be Naruto traveling back in time to the era before he was born. He could meet his parents and other important figures in the village's history. This would give him a chance to understand the roots of the village better and also learn some new jutsu or strategies that he could bring back to his own time to make the Hidden Leaf even stronger as a Hokage.
A really interesting plot could revolve around the Second Hokage's relationships. For example, his relationship with the other clans in the village. He might have to deal with the Uchiha clan's growing unrest. This could lead to him making difficult decisions to maintain the peace in the village. He could also have a mentor - mentee relationship with a young and talented ninja, guiding them to become a great shinobi.
Sasuke could be a great choice. He has powerful abilities and a complex past. His experience as an avenger and then his redemption arc gives him a lot of depth. He has also learned from Naruto and has a different perspective on leadership. He could bring a more strict and strategic approach to being Hokage compared to Naruto.
Yes, in some fanfics of 'Rokudaime Hokage', Sasuke could be depicted as a Naruto fan. Fanfic authors often explore different character dynamics, and Sasuke having an admiration for Naruto similar to a fan's view can add an interesting twist to the story.
Another aspect to explore in the fanfic is Naruto Senju's relationship with the other villages. Given his Senju heritage, there might be different expectations and tensions. He could work towards a more equal - footed relationship with other villages, instead of the traditional power dynamics. This would involve a lot of diplomatic meetings and negotiations, which could be full of drama and intrigue.