I'm not sure yet as it's a new story. But it could be new characters who discover the Death Note, or perhaps some descendants of the original characters like Light or L.
Perhaps in the 'new death note story', the Shinigami who are associated with the Death Note have changed their ways. They could be interfering more directly in the human world, either to protect the Death Note or to stop its misuse. This would add a whole new layer of conflict as humans would have to deal not only with the power of the Death Note but also with the meddling Shinigami.
It could be a young detective who is trying to solve the mystery of the Death Note's reappearance. He might be really smart and determined to stop whoever is using the Death Note for evil purposes.
Ryuk would probably just be amused. He is a Shinigami who has seen a lot in his existence. Fanfiction is just another strange human creation to him. He might chuckle at some of the more outlandish ideas in the fanfictions, like a character having superpowers beyond the Death Note.
Misa would likely be excited. She is a big fan of Light and the whole 'Kira' concept. In fanfiction, if there are scenarios where she has more power or a closer relationship with Light, she would be all for it. However, she might also get jealous if there are other female characters getting too close to Light in the fanfictions.
Well, we might expect new characters with their own complex motives. Maybe there will be a fresh take on the power of the Death Note and how it affects those who come in contact with it.
Sure. The first 'Death Note' novel is a must - read for new readers. It sets up the whole premise of the Death Note, how it works, and introduces the main characters like Light and L. It's a great starting point as it has all the basic elements that make the Death Note story so fascinating.