It could be an evil shinobi from Naruto's world who has also ended up in the Death Parade world and is trying to corrupt the system. He wants to ensure that all the souls are sent to the void or something worse, just for his own amusement or power - hungry desires.
Perhaps Naruto enters the Death Parade world in search of a lost comrade. He teams up with the arbiters, reluctantly at first, when he realizes that they have some knowledge about where his friend might be. Along the way, he shows them the power of friendship and loyalty that he has learned in the Naruto universe, and they in turn show him the complex nature of the afterlife in the Death Parade world.
One idea could be exploring the backstories of the characters in more depth. For example, the arbiter's past lives before becoming an arbiter. Another could be creating an alternate ending to the series where different decisions are made during the death games. Maybe a fanfiction where the characters from different death games interact with each other outside of the normal game settings.
Yes, there are quite a few. You can find some on fanfiction websites like Archive of Our Own. Some fanfictions explore their relationship further, showing how they grow closer and understand each other on a deeper level.
Sure, there is a manga for Death Parade. It expands on the story and characters presented in the original concept. The manga offers additional depth and details that fans might appreciate.
In a Naruto night parade fanfiction, it could involve a magical or spiritual night parade. Naruto discovers that there are spirits of the past Hokages participating in the parade. He has conversations with them, getting valuable advice on how to further protect the village and become a better ninja. The parade could also be a way to celebrate a new era of peace in the ninja world, with Naruto as the central figure leading the celebration.
Naruto, of course, is a must. Then there could be Sasuke. He might be a bit reluctant to participate at first but gets drawn into the festive mood. Sakura would also be there, perhaps helping to organize things. Kakashi could be lurking around, keeping an eye on things in his laid - back way.
The themes usually include the power of human emotions. Chiyuki's humanity and emotions start to affect Decim, so there's a lot about how emotions can change a being like Decim. Another theme is the idea of redemption. Decim might find a form of redemption through his relationship with Chiyuki, as he begins to understand the value of the souls he is judging in a different way.