The world would be in shock. The media would be filled with reports of his death. Civilians who had always seen him as a symbol of safety would feel vulnerable. There would be mass mourning in the cities he had protected.
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.
Naruto could see death magic as just another form of power that can be used for good or evil. If he witnesses it being misused, he would be angry and try to stop those using it in a harmful way. He might also try to befriend those who use it for good and learn from them. He would adapt his fighting style to incorporate defenses against death magic, like using his shadow clones to test its limits without putting himself in too much danger at first.
I often find that the best death battle fanfiction are the ones that not only focus on the fight itself but also explore the characters' emotions and motivations. It adds depth to the story. Like, a character's reason for entering the death battle could be more than just for power or glory, it could be for revenge or to protect someone they love.
The guild would be devastated. Natsu would probably be one of the first to be enraged. He'd vow to find whoever or whatever was responsible and make them pay. His fire would burn hotter than ever as he channels his anger.
Gray would be devastated. He might go into a state of deep depression, isolating himself from the rest of the Fairy Tail guild. He would blame himself for not being able to protect her, especially if her death was related to her love for him. Gray would probably be filled with anger as well, and he would vow to take revenge on whoever was responsible for her death.
Mr. Schuester would be in shock. He saw Rachel as one of his star pupils and a driving force in the Glee club. He would struggle with the guilt of not being able to protect her. He would try to keep the club going as a way to honor her memory, but it would be very difficult for him. He might also start a scholarship fund in Rachel's name for future Glee club members.
Naruto would first be extremely confused by the rules of the Death Note. His understanding of power and its consequences is rooted in his ninja training and his own moral compass. The Death Note's rules, which seem so simple yet so deadly, would be completely foreign to him. He would question why anyone would create such a thing and would be very hesitant to even consider using it, as it goes against everything he stands for in his world of ninjas, friendship, and protecting the innocent.