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.
He would probably be quite amused by some of his past antics. For example, his constant pranks on Iruka-sensei. But at the same time, he'd also see the pain he carried from not having his parents and realize how that influenced his actions. He might react with a bit of regret for some of the stupid things he did out of loneliness, but also be glad that those experiences made him who he is today.
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.
I think Midoriya could be his best friend. Midoriya is kind - hearted and always looking to learn, which would appeal to Killua. They could bond over their shared desire to become stronger and protect others.
Well, some past gods might be amused. They'd see these modern interpretations of their stories and characters in the Percy Jackson fanfiction as a strange yet interesting new form of worship or at least attention. For example, Zeus might be a bit irked at some of the liberties taken with his character, but also secretly flattered that people are still so interested in him.
Captain America would probably be very reflective. He might see his past self as a reminder of his long journey and how much he has changed. He could try to offer some words of wisdom to his younger self.
Often, they show a deeper level of commitment. The mpreg forces them to rely on each other more. For example, Gon might become more protective of Killua during the pregnancy.