Since you've already given all the answers to your own questions, allow me simply to add some historical context/explanation.
Questions 1 and 2 refer to the time in the USA known as the Red Scare.
- What historians refer to as the First Red Scare occurred from 1919 to 1921, following the end of World War 1 -- but more so following the Bolsvhevik Revolution which brought communism to power in Russia. The Bolsheviks (meaning "the Majority") were the communist faction that led a successful overthrow of the regime of the tsar in Russia in 1917. They weren't a "majority" in Russia, but they were the dominant group within the Russian communist movement. Civil war in Russia followed during the next years, from 1917 into the early 1920s, ultimately leading to the establishment of the Union of Soviet Socialist Republics (USSR) in 1922. There was fear in the United States (as there was elsewhere in the world) that communism would begin to spread further, beyond Russia.
- The more common reference to "The Red Scare" usually refers to what historically was the Second Red Scare, from the late 1940s to late 1950s in the United States. Following World War 2, as the Cold War developed and the Soviet Union was gathering allies, there was even greater fear -- and fear-mongering -- in the United States about the threat of communism. The Second Red Scare 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.
Question 3, regarding the Korean War:
- The Korean War occurred when communist forces from the North invaded the South in 1950. 90,000 North Korean troops crossed the 38th Parallel and attacked South Korea on June 25, 1950. The United Nations immediately went into action. An emergency session of the UN Security Council was held -- from which the Soviet Union was absent because the USSR was boycotting the UN over the exclusion of communist China from the organization. US President Harry Truman announced to the American people that he was authorizing sending US troops to prevent South Korea from being overtaken by communism. The UN Security Council met again and approved a US resolution approving the use of force against North Korea. Military forces in the Pacific theater, based in Japan, were deployed in the effort. There was no formal declaration of war by the US Congress, but Congress did vote to extend the draft and also authorized the president to call up military reserve personnel for duty.
- The Korean War lasted from 1950 to 1953, and about 5 million people (soldiers and civilians) lost their lives in the conflict. Korea remains divided at the same line where things stood prior to that war.