Well, I've only seen it once (and not even past that Chimera arc) but I didn't really have any of those questions. I didn't gather it was necessary to kill people in the hunter exam, just that it was possible to kill that many.
It would have been trivial to design tests that were non-fatal or had safety nets in place. There really is no justification for all the needless death we saw in the Hunter Exam. Even many of the individuals we saw fail were very skilled and either needed more training to be able to pass the test or would have been very valuable in another occupation. It's just a pointless waste to design a deadly test just to determine that someone is not good enough to be a hunter.
Moral requirement or self policing, I never gathered that was necessary. The organization (as much as it even is one) isn't based on or within any given governmental structure. Policing wouldn't be necessary, should a hunter violate the given law within a specific territory... all the government would have to do is hire another hunter (or a dozen or so) to track the offender down. Policing isn't required, because it is available for purchase.
Becoming a Hunter basically puts you above the law, and gives you a huge amount of power with no responsibilities. Beyond all of the legal and financial benefits, they also give you training to develop super powers. The leaders of the organization all seem to be morally decent people, and yet nobody seems to think that maybe keeping obvious violent psychopaths like Hisoka and Illumi out of the organization might be a good thing. I can understand not wanting to make it into another Justice League, but it's just kind of ridiculous.
How is Nen a secret when you can see it on TV... how can someone hold a patent on something that they have mass produced and sold. Looking at something isn't the same as being able to replicate it. Just because you've seen a 90 lbs person punch a 350 lbs person over a 20 foot wall, doesn't mean you'd have any idea how it was done.
I'm not talking about replicating it, but the very fact that it even exists seems to be a surprise to our entire cast, including Killua who comes from a family of Nen users. The show simultaneously treats it as a secret only known to a select few individuals and also shows it being used in televised sporting events. When are sitting in an arena and watch a guy clone himself and cut someone's arm off, which is then miraculously re-attached, I think the only conclusion that can be reached is that magic is real. This would be known and discussed by
everybody.
But yes, they totally ditched easily the most interesting plotline. They set up Kurapika's story to continue on in the Greed Island arc, and then that just went nowhere and the arc resolved itself without any further mention of phantom troupe or their leader. Hell, did they ever even pick up Leorio at any point after the... what brief mention just .... after? the tournament arc... before the tournament arc. Hell I even forgot when they ditched his entire character altogether. Apparently he just got his hunters license then got out of fighting and just became a doctor... the end.
Leorio does come back and play an active role in the arc after Chimera Ant, so if you want more Leorio you need to sit through that first. Don't get me wrong, there are some good moments in the Chimera Ant arc, but it's definitely this show's Frieza arc.