First, you need to understand the original characters well. Know their personalities, motives, and relationships. For example, the students' different assassination skills and how they interact.
One great 'assassin classroom fanfiction' story is the one where the students go on an unexpected adventure outside of the classroom setting. It really explores their characters in a new light.
Another theme could be her own growth as a character. In the series, she has her own journey, and in fanfics, this can be expanded upon. For instance, she might have to deal with personal issues outside of her teaching role, like her past relationships or her family. And how she overcomes these things can be a major part of the fanfic. It gives the author a chance to delve deeper into her character than what was shown in the original series. This can make for some really engaging stories as readers get to see a different side of her.
DeviantArt can also be a source. Sometimes, artists not only post their art but also write short fanfiction pieces related to Assassin Classroom. It might not have as extensive a collection as AO3, but the ones you find there can be really unique. They might combine art and story in an interesting way. Additionally, Reddit has some subreddits dedicated to Assassin Classroom where fans might share their favorite fanfictions or even their own works.
A great aspect is that it allows you to keep the story alive in your mind even after the anime or manga has ended. You can find fanfictions that continue the story from where it left off. Some might explore what happens to the students after they graduate. Also, reading fanfiction can introduce you to a community of fans who share similar interests. You can discuss your favorite fanfics and even get recommendations from others.
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.
There are probably some on Archive of Our Own as well. The great thing about AO3 is that it has a wide range of fanfics with different themes. In the case of Karasuma Irina fanfics, you might find some that are more centered around her character development, like how she becomes a better teacher or how she overcomes her own insecurities in the 'assassin classroom' world.
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.
Kayano would be completely devastated. Since she had a special bond with Nagisa, she might become withdrawn and filled with rage, vowing to take revenge on whoever was responsible.