Who won the Korean War?
No conclusive winner emerged. Instead, Korea returned to the "status quo ante bellum" (the way things were before the war) and North and South Korea remained divided. The US did succeed in checking Communist expansion; however, it did so at great cost in money and lives. In the larger Cold War context, the Korean War did little to improve the situation, though it also didn't lead to disintegration of relations that it could have.
Why did North Korea cross the 38th Parallel and invade South Korea?
The North Koreans were interested in attempting to reunify Korea under Communist rule, and Stalin most likely gave his approval for the invasion, perhaps as a test of how the US would react (or, as some have hypothesized, a test run for Berlin?). Regardless, the North Koreans were armed with Soviet T-34 tanks. Also, US speeches and policy at the time suggested to the North Koreans and the rest of the Communist world that Korea was not vital to American security and interests.
How did American politics effect the war?
Truman, a Democrat, was afraid of appearing "soft on Communism", lest his Republican opponents attack him. McCarthyism in particular, a rampant paranoid anti-communism sweeping the US, created a particularly hysterical anti-Communist environment. Wihtin this context, though General MacArthur (not to be confused with Senator Joseph McCarthy, who was unrelated) often acted insubordinately, Truman could not take action against him because the general was so popular with the Republicans. In fact, only the combined support of the Joint Chiefs of Staff saved Truman from impeachment after he fired MacArthur. Truman could not negotiate easily with the Communists either, for fear of Republican criticism. Only Eisenhower, a Republican President, was able to make concessions to Chinese and Panmunjom, managing to get a weak treaty signed without criticism.
Why did the US intervene in Korea when it did not intervene in China?
Having just seen China fall, US policymakers had a heightened sensitivity to Communist threats, and considered the North Korean invasion to be a possible test-run for an invasion in Eastern Europe. According to the logic of NSC- 68, a communist attack anywhere should be viewed as an attack everywhere. Under that logic, Korea became "as good a place to draw the line as anywhere."
Describe the role of the UN in the Korean War.
The UN was basically a policy instrument of the US during the Korean War. Especially with the USSR boycotting most UN proceedings, the US used its powerful influence to shape UN policy to meet its own individual needs. The UN International Peace-Keeping Force, made up mostly of American troops (and a few NATO troops), was really just a sham engineered to give the appearance that support for South Korea was more than just a unilateral American action.
Was the Korean War an international war or a Civil War?
Certainly many nations were involved in the Korean War, and in that sense it was a very international war. However, one should remember that Korea had been divided arbitrarily by the US and the USSR after World War II. The 38th Parallel was a made-up boundary with no historical precedent or resonance, and so, in a sense, the North Korean attack might be considered part of an internal, civil war to unify a single country that shared the same culture and language and had historically been unified. It was because of this somewhat ambiguous nature of the Korean War that the UN classified the attack by North Korea as a "breach of peace" rather than a far worse act of "aggression".
Why did the negotiations to end the Korean War go on for so long.
The negotiations at Kaesong and then Panmunjom dragged on for so long (about 2 years) primarily because neither side was willing to make concessions for fear of appearing weak. Specific issues included the fate of Formosa (Taiwan), the dividing line between North and South Korea, and the question of what to do with POWs (Prisoners of War).
Why did the PRC (People's Republic of China) cross the Yalu and start a counteroffensive against the US/UN/ROK forces?
As MacArthur's forces pressed North across the 38th Parallel, the Chinese Communists feared an invasion of Manchuria. Furthermore, MacArthur's meeting with Truman at Wake Island suggested to PRC leaders that a major US offensive was in the works, perhaps a plot to restart the Chinese civil war.
What was the result of Truman's firing MacArthur.
General Ridgway replaced MacArthur as Commander of the Far East. Ridgway held a more conservative stance, followed orders from Washington readily, and did not seek to expand the war as haphazardly as MacArthur did. However, Truman's dismissal of MacArthur upset many MacArthur-loving Republicans in Congress, who threatened to impeach Truman. Fortunately for him, Truman had the unanimous opinion of the JCS behind him, so he wasn't impeached. In the long run, Truman's reliance on the Joint Chiefs of Staff increased the group's power in military decisions over the future Presidents.
Was strategic bombing effective during the Korean War?
For the most part it was not. North Korea was simply not industrialized enough for strategic bombing to have a devastating impact. The infrastructure (especially bridges and roads) that strategic bombing did manage to destroy were usually quickly rebuilt by North Korean laborers. In negotiations as well, strategic bombing, even that aimed against dams and power plants in northernmost Korea, failed to win concessions, and may actually have hardened the resolve of the Communists.