To stop the communist forces from reuniting Korea under a communist government
It was called a "police action"
South Korea.
Stop communist aggression.
Korea had been taken over by the Japanese prior to the war. Thus, one goal of the Allied Pacific war was to liberate Korea from Japanese control. Korea was not an enemy of the Americans; it was more of the damsel in distress.
Easily, but such an action would trigger an attack by China on the US in retaliation and we would have a full blown nuclear war.
Korea
South Korea
To stop South Korea from becoming communist.
North Korea has issues with the US. But the US does not hate Korea. The US has a strong and very old alliance with China that makes then stronger than Korea.
Russia walked out of the UN so the US was able to get UN to agree to send troops to defend South Korea. The active fighting stopped after 2 years, but no peace treaty was ever signed.
South Korea
No. The US leads the world in enforcing sanctions against North Korea.