Short answers, pulled from the story.
The Korean Armistice Agreement was signed on the 27th of July 1953 by Lieutenant General William K. Harrison Jr. for the United Nations Command and General Nam Il for the Korean People's Army and Chinese People's Volunteer Army. Peng Dehuai signed representing the Chinese People's Volunteer Army, and North Korean leader Kim Il Sung also signed. South Korea did not sign the agreement.
South Korea refused to sign because President Syngman Rhee would not accept an agreement that left Korea divided. Rhee had sought to unify the peninsula by military force, advancing to the Yalu River, and viewed the armistice as a failure to achieve that goal.
The Korean Demilitarized Zone is a 2.5-mile-wide fortified buffer strip established by the 1953 armistice. It follows the Kansas Line, the position where both sides stood at the moment of signing, and runs close to the 38th parallel. It is currently considered the most heavily defended national border in the world.
North Korea has announced it would no longer abide by the armistice at least six times: in 1994, 1996, 2003, 2006, 2009, and 2013. A United Nations spokesman stated that the agreement, having been adopted by the UN General Assembly, cannot be unilaterally dissolved by either Korea.
The Geneva Conference convened in April 1954, six months after the armistice's three-month deadline for a political settlement. Chinese diplomat Zhou Enlai formally proposed a peace treaty on the Korean peninsula to US Secretary of State John Foster Dulles, but no progress was made. The United States deliberately avoided discussing a formal peace treaty despite criticism from other conference participants.
Paragraph 13d banned either side from introducing new weapons into Korea beyond piece-for-piece replacements. At a Military Armistice Commission meeting on the 21st of June 1957, the United States formally declared it no longer considered itself bound by that clause. By January 1958, nuclear-armed Honest John missiles and 280mm atomic cannons had been deployed to South Korea, followed by Matador cruise missiles capable of reaching China and the Soviet Union.