Interesting. I did not know that. I am shocked that we would be allowed to inspect most nuclear powers. (I just can't conceive of China, N. Korea, Russia or Pakistan allowing us to inspect. Heck, I doubt France and England would. Who am I missing? India? (Anyone else?)) I would hope that we don't let those countries inspect our nuclear arsenal.
Yes, I think it is a large reason for this thread. But, I also don't know how effective those agreements are. I remember Pakistan (Pakistan!) getting a bomb in the 90s, and more recently, North Korea.
I don't know, but I remember people speculating that Israel had a bomb when I was in school in the 80's, so I think that if they got a "pass" it was a long time ago. I suspect they would have gotten the ability the way many countries did - espionage.