Minato might inherit Naruto's chakra - related abilities. So he could have access to a large amount of chakra and be able to perform powerful ninjutsu like the Rasengan. Since he has Naruto as a father, he could also potentially have some sort of connection to the Nine - Tailed Fox. And from Bulma, he could inherit a high intelligence. This would allow him to understand complex scientific concepts quickly, which he could use in combination with his ninja skills, like creating new types of jutsu using scientific principles.
He could inherit Naruto's chakra - rich nature. So, he might have a large reserve of chakra like his father. Also, since Naruto has the Nine - Tails' chakra, Minato might have some sort of unique connection to it as well, perhaps being able to access a small portion of its power in a different way than Naruto does. And of course, he could inherit some of Naruto's signature jutsu like the Rasengan, but with his own twist.
Minato would likely be extremely shocked. Naruto is his son, and the idea of Naruto attacking him would be completely unexpected. He would probably try to talk to Naruto first, to find out what is wrong and why he is being attacked.
One of the main similarities is their self - sacrifice. Minato sacrificed himself to save the village and his son. Naruto has also shown that he is willing to put himself in harm's way for the greater good. He's always the first to jump into a dangerous situation if it means protecting those he loves. Another aspect is their leadership qualities. Minato was a great leader as Hokage, and Naruto has developed into a great leader as well, inspiring those around him.
The emotional bond would be stronger. Naruto wouldn't have to face the pain of growing up without a father. Minato could be there to cheer him on during his training and be a source of comfort when Naruto faced difficulties, like when he was bullied as a child. He could also help Naruto better control the Nine - Tails' power from the start.
Well, Minato might constantly be by Naruto's side in the fanfiction. He could prevent Naruto from taking on any dangerous missions, even if Naruto is capable. For example, he may interfere when Naruto tries to join a risky battle against a powerful enemy, saying it's too dangerous for him.
One reason could be guilt. Since Minato wasn't there for Naruto when he was growing up in the original story, in the fanfiction, he might be overcompensating for that lost time. He feels like he has to make up for all those years he wasn't around to protect his son.
Minato could also teach Naruto about leadership. As the Fourth Hokage, he led Konoha. He could share his experiences on how to make tough decisions for the good of the village and its people. He might tell Naruto stories of past battles and how he strategized to win, which would help Naruto in his future as a leader in Konoha.
Kushina could be an important character even though she's dead in the original story. In this fanfic, her spirit or memories could play a role in Naruto's upbringing. For example, Minato could tell Naruto stories about Kushina's feisty personality and her love for the village.