One unique feature is the blend of different fictional universes. Naruto's world of ninjas and Okumura's world are quite distinct, and in these fanfics, seeing how the two worlds' elements merge is really interesting. For example, in some fanfics, Okumura's powers interact with Naruto's chakra in unexpected ways.
One popular 'Naruto Okumura fanfic' could be 'Naruto and Okumura's Adventure'. It has an interesting plot where Naruto and Okumura team up to face a new threat in a world that combines elements from both their original universes. The character interactions are well - written, especially how Naruto's positive attitude influences Okumura.
In 'angel rin okumura fanfic', a significant theme is power. Rin's angelic powers are often explored, how he gains more control over them, or how they evolve. Family also comes up as a theme. His relationship with his family, especially his angelic heritage, is a big part of many stories. Moreover, the theme of redemption can be found. As an angel, Rin may try to redeem some of the wrongdoings associated with his demon side in some fanfics.
However, in the realm of fanfiction, anything can happen. A writer could create an elaborate backstory where Naruto somehow ends up in the Blue Exorcist world and becomes Rin's father. Maybe there could be some sort of interdimensional travel or a really wild magic spell that links the two universes in a way that makes this relationship possible. But it would require a lot of creativity to make it believable within the context of the combined universes.
One common theme is the exploration of their opposing natures. Amaimon is often depicted as chaotic and unpredictable, while Rin is more of a determined hero type. Their interactions based on these differences are frequently explored.
Another great one is 'Cute Moments with Rin Okumura'. This fanfic is a collection of short stories about Rin. It includes things like his attempts to cook for his friends at the True Cross Academy and the resulting chaos that is still somehow really cute.
Fanfiction.net is also a good place. Just search for 'Rin Okumura' and then filter through the results to find the ones that seem to have a 'cute' theme. There are often reviews that can help you determine if it's the kind of cute story you're looking for.
A great plot idea for a fanfic involving them could be a crossover tournament. They are both dragged into a mysterious tournament where they have to fight against various opponents from different dimensions. Along the way, they start to understand each other's strengths and weaknesses and develop a mutual respect.
The story could also focus on the family dynamic. Naruto, being a very determined and positive character, could be a great father figure to Rin. He could encourage Rin to face his inner demons (both literally and figuratively) with the same kind of courage that Naruto has. And perhaps Naruto would have to protect Rin from the more dangerous aspects of the Blue Exorcist world using his ninja abilities.
Yes, there are some. You can start by checking fanfiction websites like Archive of Our Own. There you might find various stories featuring this pairing. Just use the search function with the relevant tags.