Well, first of all, Minato would likely be shocked. Naruto's past was full of hardships and loneliness. Minato would probably experience a mix of emotions. He might be sad that Naruto had to endure so much pain. He could also be proud of how Naruto overcame all those difficulties and still managed to grow into a strong and kind - hearted person. He might even try to find ways to comfort Naruto in this fanfiction world, like giving him some long - lost family memories or advice that could have made his journey easier.
The aftermath could be Minato's quest for revenge if Naruto's death was caused by someone. He would use his skills and knowledge to track down those responsible. Or, he could be plunged into a deep depression. He might isolate himself from the other spirits or entities in the afterlife. His whole existence could become centered around his grief and his memories of Naruto.
Minato would likely be devastated. He sacrificed his life for Naruto, hoping for a great future for his son. Seeing Naruto die would shatter his hopes and dreams. He might first be in denial, unable to believe what he's seeing. Then, his grief could turn to anger, either at the situation or at those he believes are responsible. It's a tragic scenario that would change Minato's afterlife perception and his sense of purpose, which was always tied to Naruto's well - being.
One possible plot development could be that Minato uses the knowledge of Naruto's past to help him train better. Maybe he reveals some hidden family jutsu or techniques that Naruto can use to become even stronger.
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.
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.
In some fanfictions, Minato saves Naruto physically. For example, he might use his teleportation jutsu to appear right in the middle of a fight and whisk Naruto away from danger. In others, he could save Naruto spiritually. He might enter Naruto's mind, like in the fanfic 'Minato's Mind - Saving Mission', and give him the strength and confidence to overcome his inner demons. Sometimes, Minato saves Naruto from a political situation. For instance, in 'Minato and the Hidden Leaf's Politics', he uses his influence and wisdom to protect Naruto from being used as a political pawn.
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 common ability is their speed. Minato was known as the Yellow Flash for his incredible speed. Naruto, with his Sage Mode and later forms, can also move extremely fast. Another is their use of the Rasengan. Minato created the Rasengan, and Naruto has mastered it and even developed it further.
One possible reason could be for Naruto's protection. Maybe Minato knew of some great danger that was coming for Naruto and he thought that banishing him would keep him out of harm's way. Another reason might be related to some prophecy or hidden power within Naruto that Minato feared could be misused if Naruto stayed in the village.