A common theme is family. Given their complex family situation in the original story, fanfictions often explore how Killua and Alluka's relationship affects and is affected by their family. Another theme is protection. Killua is very protective of Alluka, and this is often a central aspect in these fanfictions.
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.