Short answers, pulled from the story.
The Korean War started on the 25th of June 1950 when the Korean People's Army crossed the 38th parallel at dawn. This surprise invasion ignited a global conflict that drew in the Soviet Union, China, and the United Nations.
North Korea was led by Kim Il Sung in Pyongyang while South Korea was led by Syngman Rhee in Seoul. Both leaders claimed to be the sole legitimate government of all Korea, setting the stage for a three-year war.
The Inchon landing occurred on the 15th of September 1950 and was recommended by General Douglas MacArthur to cut off North Korean troops and supply lines. This amphibious operation involved 40,000 troops of the 1st Marine Division and 7th Infantry Division along with 8,600 ROK soldiers.
The Chinese People's Volunteer Army crossed the Yalu River on the 19th of October 1950 to enter the war on the side of North Korea. Their entry changed the attitude of the Soviet Union and led to heavy losses for UN forces during battles like the Battle of the Ch'ongch'on River.
Combat ended on the 27th of July 1953 with the signing of the Korean Armistice Agreement. This agreement allowed the exchange of prisoners and created a Demilitarized Zone along the frontline with a Joint Security Area at Panmunjom.