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.
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.
You can try looking on popular fanfiction websites like FanFiction.net or Archive of Our Own (AO3). They usually have a wide range of Naruto - related fanfictions, and you should be able to find some with the 'Team Minato Watches Naruto vs Pain' concept.
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.
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.
I'm not sure if there is such a specific fanfiction. Fanfiction can cover a wide variety of themes and scenarios, some of which might be rather strange or controversial. However, Naruto fanfiction often explores different relationships and alternate storylines, but this particular one seems a bit unorthodox and I haven't personally come across it.
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.