Question 1:
In the Cold War, the United States (USA) and the Union of Soviet Socialist Republics (USSR) were at odds with each other because of strongly different worldviews. The USA was committed to capitalism and democratic institutions of government, whereas the USSR was committed to communism and imposed authoritarian government. Initially, the USA had atomic weapons and the USSR did not. (The US would not share that technology with the Soviets, who had been their ally in World War II.) But once the Soviets developed their own atomic weaponry, this led to a massive arms race between the superpowers. The two nations kept escalating their weapons capabilities and stockpiles. It got to the point that if the two sides did plunge into war, they would face mutually assured destruction. John Foster Dulles, the Secretary of State under President Eisenhower, wanted a change from what had been the "containment policy" which the US had followed during the Truman Administration, as recommended then by American diplomat George F. Kennan. Dulles felt the containment approach put the United States in a weak position, because it only was reactive, trying to contain communist aggression when it occurred. Dulles sought to push America's policy in a more active direction; some have labeled his approach "brinkmanship." In an article in LIFE magazine in 1956, Dulles said, "The ability to get to the verge without getting into the war is the necessary art." He wasn't afraid to threaten massive retaliation against communist enemy countries as a way of intimidating them.
Eventually (after decades of the arms race and tensions) the US and USSR would pursue policies of detente, which included pledges to reduce their nuclear arsenals. The arms race and solving the arms race were constant issues affecting the Cold War.
Question 2:
Following World War 2, as the Cold War developed and the Soviet Union was gathering allies, there was much fear -- and fear-mongering -- in the United States about the threat of communism. This time period, from the late 1940s to late 1950s, is known as the Second Red Scare. This was when the House Un-American Activities Committee (HUAC) was created and when Senator Joseph McCarthy began a campaign of accusations against suspected communists in various sectors of American life. During the Second Red Scare, many people were targeted -- including especially those in the entertainment industry, journalism, and in government and the military. The lessons learned from the McCarthy era showed that the freedoms guaranteed in the Bill of Rights must be vigorously defended. If individual's rights to freedom of speech and freedom of association are called into question, and due process of law is not followed, everything America stands for can come under attack.
A good film you might look for on the subject of McCarthy's fear campaign and how it was overcome is the 2005 movie, "Good Night and Good Luck." The film shows the efforts of journalist Edward R. Murrow to battle against McCarthy's excesses and unfounded accusations. It was especially through the efforts of Murrow that McCarthy's excessive actions were stopped.