He might become very withdrawn. Bell could start to isolate himself from others, especially those associated with Hestia. He may no longer trust as easily as he did before.
Killua is likely to be completely devastated. He might go into a state of shock at first, not believing that Gon is really gone. Then he could become very angry, either at himself for not being able to protect Gon or at the situation that led to Gon's death.
Gon in fanfiction can be very single - minded in his pursuit of goals, just like in the original. He might be a bit more naive at times, which can lead to interesting plot twists. Killua is often portrayed as having a complex emotional side. He struggles with his past as an assassin and his loyalty to Gon. His cool exterior may crack in some fanfictions, showing his true feelings.
The gods would have a variety of reactions. Some might see it as a sign of something special, perhaps a new era beginning. Others might be more cynical and think it will bring trouble. For example, Freya might be interested in the child's potential and keep a close eye on the family. Zeus, if he were still around, might offer his wisdom on raising a child with such unique parentage. And Hermes could spread the news far and wide among the gods and mortals alike.
In a Naruto world fanfic, Killua would bring a whole new dynamic. He has a dark past as an assassin which could either make him a feared or respected figure. His family's training has made him physically and mentally tough. In battles, he could use his electricity - based attacks in creative ways against ninjas. But he would have to learn about things like jutsus and the ninja villages. Also, his relationship with Gon in the HxH world was important for his character development, and in the Naruto world, he might find a similar bond with a fellow shinobi, which could change his perspective on things.
Yes, there are likely some fanfictions out there with such a concept. Fanfiction writers often come up with creative crossovers. You can try searching on popular fanfiction websites like Archive of Our Own or Fanfiction.net.
He could form a rival - like relationship with Sasuke. Both are highly skilled and have a bit of a dark side. They might constantly compete to prove who's better in combat.