Well, in kurapika and neon fanfiction, a common theme could be the contrast in their worlds. Kurapika is from a tragic background with his clan's destruction driving him. Neon, on the other hand, is a part of a wealthy and powerful family. Fanfic writers may play with the idea of how these two from such different walks of life come to understand each other. Maybe Kurapika sees in Neon a glimmer of innocence that he wants to protect, or Neon could be intrigued by Kurapika's mystery and strength.
If we consider a gender - swapped Kurapika in a fanfic, it could have a significant impact on the story arc. For example, if Kurapika was female, her emotional journey might be perceived differently. Her anger and determination for revenge could be seen as more of an underdog story, as in some fictional universes, female characters are often underestimated. This could add more depth to her character as she overcomes these biases.
I don't think so. There haven't been any official announcements or indications that the HxH manga will continue. But you never know, maybe there'll be a surprise in the future.