Short answers, pulled from the story.
The New Look was the national security policy of the United States during Dwight D. Eisenhower's presidency. It emphasized reliance on strategic nuclear weapons and covert operations over expensive conventional forces, reflecting Eisenhower's belief that military spending must remain compatible with the health of the U.S. economy.
Eisenhower approved NSC 162/2 on the 30th of October, 1953. It formalized the New Look's "long-haul" approach to national security, maintaining a steady level of military preparedness without the economic strain of massive conventional spending.
Massive Retaliation was the core military doctrine of the New Look, summarized by the slogan "more bang for the buck." Secretary of State John Foster Dulles proclaimed it before the Council on Foreign Relations on the 12th of January, 1954, stating the United States would respond to aggression at places and with means of its own choosing, including nuclear strikes.
Historian John Lewis Gaddis argued Massive Retaliation lacked credibility against "less-than-total challenges," citing the Soviet intervention in the 1956 Hungarian Revolution as an example. The doctrine's credibility also diminished steadily as Soviet strategic nuclear power grew, and it theoretically gave the Soviets an incentive to strike first.
Green Light Teams were U.S. commandos trained in secret exercises in which they carried actual nuclear weapons. Their missions were to infiltrate targets, detonate the weapons, and be exfiltrated, though many understood they were effectively being sent on kamikaze missions.
NSC 5440, approved as NSC 5501 on the 7th of January, 1955, replaced Massive Retaliation with an emphasis on applying force selectively and flexibly. Historian Campbell Craig described it as the precise articulation of the strategy of flexible response, seven years before that term came into common use.