Minato's presence would likely make them closer. He'd encourage them to see each other as brothers. Since Minato is Naruto's father, Naruto would have more confidence and be more at ease, which would make Sasuke respect him more. They'd have a common figure to look up to and follow his teachings together.
I think young Sasuke would have a very intense reaction. He was so consumed by his hatred for Itachi at that young age. A Sasuke vs Itachi fanfiction would be like a trigger for him. He would be eager to see how the fictional fight is portrayed. If Sasuke in the fanfiction is shown as strong, it might fuel his own ego and make him strive even harder to become powerful. However, if the fanfiction shows Itachi as superior, it could enrage him. He might feel that it undermines his own goal of defeating Itachi and he might even want to find the writer to correct their 'wrong' view.
It's really hard to say. Minato is extremely fast with his Flying Raijin and is a very intelligent fighter. But Naruto has an incredible amount of chakra, his Sage Mode, and his Six Paths powers. If Naruto can get close enough to Minato, his brute strength could overpower Minato. However, Minato's speed and strategic mind might keep Naruto at bay.
In some 'minato vs naruto fanfiction', there could be a scenario where they battle in a different dimension. Minato uses his Flying Raijin to quickly move around and Naruto counters with his shadow clones and massive Rasengan attacks. Also, a scenario where they fight not as enemies but in a friendly spar to teach Naruto some secret family jutsu that only Minato knew would be really cool.
One possible plot could be Minato teaching Naruto and Sasuke his signature jutsu, like the Rasengan. He'd pass on his skills and wisdom, guiding them to be stronger and more responsible ninjas. Naruto might learn about his father's past more directly from Minato, and Sasuke could gain a new perspective on family and loyalty through Minato's influence.
I like Naruto in these fanfics because he always stays true to his beliefs. He is constantly trying to bring Sasuke back to the village and is willing to fight for their friendship.
One of the best moments is when they have a rematch that showcases their growth. Naruto has become stronger with his new jutsu, and Sasuke has further mastered his Sharingan powers. The intense battle of ideologies during the fight is captivating.
There are many out there. A really good one might focus on the emotional reactions of Team Minato. For example, Minato might be proud of Naruto's strength and how he overcomes Pain. Kakashi could be in awe at Naruto's new techniques. Their reactions can enhance the overall viewing experience in the fanfiction.
It really depends on the writer's preference. Some fanfictions might have Naruto winning because of his unwavering belief in friendship and his ability to draw on the power of the nine - tails. Others might have Sasuke winning due to his strategic mind and mastery of the sharingan.
It's not clearly stated in the original Naruto series that Konoha as a whole watches Naruto vs Sasuke fanfiction. Fanfiction is a creation of the fans outside the official story. However, it would be an interesting concept to think about. Some characters might be amused or even inspired if they were to read such fan - created stories, but there's no in - canon evidence for it.