Damn I really want to know what happened to kurapika during the chimera ant arc. Did he just fail his bodyguard duty and then take over the family out of necessity or did he kill his boss to take over?
It's probably the former.
The Nostrade Family had only gained power because of the Neon's fortunes. So things likely went downhill right after Yorknew City. Mafias can have family successors but it's not guaranteed, sometimes the right hand man or the boss's favorite becomes boss. so Kurapika was either a Right Hand Man/Favorite and was given the position, or both the head of the family and Neon was killed.
We don't know for sure about the dad but we just got confirmation about Neon dying. : (
Also LOL Illumi's introduction was amazing.