First Issue:
Because of the destructive nature of nuclear weapons, obviously I would rather no one have them. But in reality, the cat is already in the bag and because competing nation states have nuclear weapons in their possession, they would likely never relinquish them all because of the fear the another nation state was lying and held some back in their possession. As for unstable people getting access that are in government, you should research the current safeguard we have in place so that only a few men have the ability to arm and launch nuclear weapons and those people are vetting quite harshly and are given continual physiological evaluations you mental stability.
And we can't have everyone agree not to own nukes and police each other for it, while having a private defense force in charge of keeping out outsiders, whom we entrust with owning a nuke for deterrent reasons because...?
Second Issue:
That is an assumption they would be found out, if you know what your doing you could be covert about it. There are small tactical nukes are are as small as a suitcase. Also in your example, you gave a price tag so I had to assume that person was purchasing it from somewhere not building their own. Building your own it a whole other ball game and is very hard to mask because of the equipment needed, power consumption and raw materials. You really need to understand, covert action happens everyday and it is effective more times than not. History is filled with examples (that we know of) and it is only decades if not longer that we find out, or we seize records and read about them after the fact.
If someone sold someone a nuke, then they know whom they sold the nuke to. If one of those nukes does go off, either whoever sold the nuke will have told everyone whom they sold that one to, or they would be held responsible. And yes, the price tag is the estimates cost of a nuke on the black market. But, regardless, why is covert action and black market suitcase nukes a problem in anarchy state, but not a problem in government controlled state? What makes people with a government paycheck different or better than people with a private company paycheck?
1. This is where you need to take in the current situation and when we are talking about someone like this, it is all the matters. Like I said, this cat is out of the bag. I would rather have the current governments safeguard the nukes then proliferate them to a point where someone who is dis-satisfied decides to use them and kill innocent people to try and prove a point or achieve their goals.
2. Why do you think the person would say anything, another speculation with no reason to believe that it is the case. Maybe the person selling it, gets informed about its end use and supports it so they are glad it happens. Another option is that it could change hands. I never said this was an anarchy state only problem, where did you get that from? You are so caught up in your idea of Anarchy that you assume someone who doesn't support it is so colored in their thinking that they would think in that manner. I keep seeing interesting patterns debating with you all, quite interesting.