This was the best animated struggle a person had with himself that I've seen for a long while. Though I wish the backstory DE was referring to had been there, so that this scene would have been more meaningful. So that Kite would really have been a personally important person for Gon, because that's what this episode was all about.

I'm not so sure Killua believes Kite can be saved. He's the more pessimistic of the two usually. But he might have wanted Gon to remain a better person by placing even a slim hope of saving a friend above quick revenge executed in fury. Killua will forever be an assassin, but I reckon a part of why he values Gon so much is that Gon isn't a killer by nature.

I also don't see why Pitou would honour anything she might promise to Gon. Only the king matters to her. Her personality is kind of a product of serving the king as well. Unless she thinks she's serving the king, in some manner, by leaving with them, she ought to ignore the whole thing afterwards and try to get rid of Gon & Killua. If the king is still away at that point and thus not in a position to override any of her decisions, I reckon a slight chance could be that since the king wanted to save a human, Pitou could extrapolate from that she should also honour an agreement with humans.