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.
The plot might involve Naruto crying due to a misunderstanding with his friends. Kakashi witnesses this and steps in to mediate. He first calms Naruto down and then arranges for Naruto and his friends to have an open conversation. During this process, Kakashi shares some wisdom about friendship and communication, helping them resolve their differences.
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.
Well, one similarity could be their determination. In the fanfic, like in the original series, both Naruto and Kakashi are very determined. Naruto is always striving to become Hokage and Kakashi has his own goals and missions he's dedicated to. They also might share similar combat styles in the fanfic, perhaps Naruto starts to adopt some of Kakashi's strategic thinking during battles.
In fanfiction, Naruto and Minato often represent a connection between generations. Minato was a great ninja in his time, and Naruto is following in his footsteps. Fanfictions can explore how Naruto lives up to his father's reputation.