One idea could be that Deadpool somehow gets transported to the Naruto universe. He'd be really confused at first but then start causing all kinds of chaos with his unorthodox fighting style and fourth - wall - breaking humor. Maybe he'd try to team up with Naruto, thinking he could use some of Naruto's cool jutsu in his own battles back home.
A third common theme is the chaos that Deadpool brings into Naruto's world. Deadpool is unpredictable and often causes mayhem in the usually orderly (in its own way) ninja world. This upheaval and how the Naruto characters deal with it is a major theme in many of these fanfics. Sometimes it's played for laughs, other times it's used to explore deeper concepts about order and chaos.
Deadpool would likely be a very chaotic element in the Naruto world. In a fanfic, he might arrive through a portal that was opened accidentally. His combat style would be completely different from what the ninjas are used to. He doesn't really have a set of jutsu like the ninjas, but his acrobatic fighting and use of guns and swords would be a novelty. He could form an unlikely friendship with Naruto. Naruto would be intrigued by Deadpool's immortality and try to understand it, while Deadpool would be interested in Naruto's chakra and the whole concept of ninjutsu.
It's hard to say. Naruto has his powerful jutsu like the Rasengan and his Nine - Tails chakra. But Deadpool is almost unkillable. If Naruto couldn't figure out a way to completely destroy Deadpool, Deadpool would keep coming back for more and eventually wear Naruto down with his unpredictable attacks.
One great 'naruto and deadpool fanfic' is 'The Unlikely Team - Naruto and Deadpool'. It combines the unique humor of Deadpool with the ninja world of Naruto in a really interesting way.
In this fanfic, perhaps Deadpool's training makes Naruto question his own beliefs and values. Naruto has always been about friendship and protecting the village, but Deadpool's chaotic nature might make him see things from a different perspective. As Naruto becomes more 'godlike', he has to balance his newfound power with his original ideals, and this internal struggle could be a major part of the story.
Obviously, Naruto and Deadpool would be the main characters. Naruto is the one being trained and evolving into a 'godlike' state. Deadpool is the trainer who brings his own set of skills and personality to the story.
Deadpool is crazy and unpredictable, often doing things for his own amusement. Naruto is more about friendship and protecting his village. So Deadpool might do things that Naruto thinks are irresponsible, like attacking enemies without a plan just for fun.
Yes, there probably is. There are many fanfiction platforms where writers combine different universes. Since both Naruto and Deadpool are popular characters, it's likely that someone has written a fanfic about Naruto being a Deadpool fan. You can check websites like FanFiction.net or Archive of Our Own to find such works.