Okay, one by one, to finally put this shit to rest:
In HxH, potential is an actual thing, a legitimate cap to an individual’s skill that can be reached through intense training. Gon happens to have an incredibly high potential by winning the genetic lottery and being Ging’s son. Thus, he is able to sacrifice his potential using enhancement nen to dramatically speed up his maturation factor, achieving Gon-san but also destroying himself. Everything here is logically consistant.
The Queen only needs to eat the brain of a human for them to be reborn, and the many injuries around the top of kite’s head are enough to suppose that Pitou gave his brain to the Queen, but kept puppeting his body for nen-unlocking purposes.
As the Zoldycks’ greatest prospect, Killua was left to learn nen by himself. This line of thought is why Silva let Killua leave in the second arc, he (and Zeno) seem to think that it’s best for their most promising to go out and master nen on his own. As they don’t place as much stock in the rest, they don’t have any reason not to just teach them nen, it’ll help with their jobs after all.
Killua has legitimate emotional issues, and they haven’t even been fully resolved at the end of CA or the election. I suspect they’ll be put to rest in the arc when he and Gon finally return to the story. However, there was clearly something more going on with Illumi, just look at how easily he was totally manipulated at the end of the Hunter exam. The needle’s existence explains the supernatural influence Illumi holds over Killua’s mind, without magically resolving all of his issues. Killua still feels inadequate through the palace invasion (see his reactions to Gon and his breakdown) and even to the end of the election, although Alluka cheers him up a bit.