Short answers, pulled from the story.
The Castle Bravo test released a yield of 15 megatons, which was more than double the expected power. This event became the worst radiological incident in US history and sickened crew members aboard the Lucky Dragon ship.
The treaty formally went into effect on the 10th of October 1963 after being signed by the Soviet Union, United Kingdom, and United States in Moscow on the 5th of August 1963. Since then, 123 states have become party to the agreement while ten others have signed but not ratified it.
James Fisk led the US delegation while Evgenii Fedorov represented the Soviets and William Penney headed the British team. The conference declared it technically feasible to establish an effective control system on the 21st of August 1958.
John F. Kennedy linked continued testing directly to nuclear proliferation calling it the Nth-country problem because he warned that if China or France successfully tested atomic bombs, security for both Russians and Americans would dangerously weaken. He assumed presidency in January 1961 committed to advancing comprehensive test ban negotiations.
Khrushchev insisted three inspections yearly must be limit since anything more frequent constituted espionage. He privately believed allowing three inspections significant concession as other Soviet officials preferred less intrusive systems.