One idea could be that as Minato is dying, he passes on his special jutsu knowledge to Naruto in a final moment of father - son connection. Kushina, on the other hand, tries to comfort Naruto while also mourning Minato.
Time - travel is also a frequent theme. For example, Minato might be brought to the present or Naruto sent back in time to meet his father. This allows for a lot of interesting interactions and character development. And of course, the theme of mentorship is there. Minato was a great shinobi, and fanfics often show him mentoring Naruto and passing on his skills and wisdom.
Another good one is 'Hidden Feelings'. In this fanfic, the author slowly builds up the relationship between Minato and Naruto. It starts with small interactions and gradually develops into something deeper, with great character development along the way.
Good Minato x Naruto yaoi fanfic often has well - developed characters. It should stay true to the personalities of Minato and Naruto from the original Naruto series. For example, Minato's calm and intelligent nature and Naruto's energetic and determined self.
If Minato didn't die in the fanfiction, he could have been a great mentor to Naruto. He could have taught Naruto advanced ninjutsu much earlier, and Naruto might have become even more powerful at a younger age.
One common theme is redemption. Minato often gets a chance to make up for things he couldn't do in his original timeline. Another theme is the strengthening of the father - son bond. Since Naruto and Minato didn't have much time together in the original story, time travel allows them to form a deeper connection.
One popular 'Minato x Naruto fanfic' is 'A Father's Love Revived'. It beautifully explores the relationship between Minato and Naruto in a way that shows Minato getting a second chance to be in Naruto's life and guide him. Another great one is 'Minato's Return'. It has a really interesting plot where Minato returns and has to deal with the modern shinobi world while reconnecting with Naruto.
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.
Well, it depends on the specific fanfic. Some fanfics might really emphasize Naruto's growth to be on par with Minato in terms of smarts. They could show Naruto learning from Minato's memories or having some sort of spiritual connection that transfers knowledge. However, other fanfics might focus more on other aspects of Naruto's character and not necessarily make him as smart as Minato.