Short answers, pulled from the story.
The Hungarian Revolution of 1956 began on the 23rd of October 1956 in Budapest and was crushed by Soviet forces on the 4th of November 1956. Fighting outside Budapest continued until at least the 12th of November; the entire uprising lasted 15 days.
Approximately 2,500 Hungarians and 699 Soviet soldiers were killed in the repression of the revolution. Around 20,000 Hungarians were wounded. About half of all Hungarian casualties were people younger than thirty, and roughly 53 percent of the dead were workers.
The USSR launched its second intervention because Nagy's declaration of Hungarian neutrality and withdrawal from the Warsaw Pact broke the buffer zone of satellite states protecting Soviet territory. Khrushchev also faced pressure from hardline CPSU members, from the Chinese leadership including Mao Zedong, and from concerns that multi-party democracy in Hungary and Poland would undermine communist authority across Eastern Europe.
Nagy took refuge in the Yugoslav embassy after the Soviet assault. Despite Soviet and Kádár government promises of safe passage, he was arrested on the 22nd of November 1956 when he attempted to leave the embassy and was taken to Romania. He was executed after secret trials in June 1958, and his body was placed in an unmarked grave in a municipal cemetery outside Budapest.
Approximately 200,000 Hungarians fled as refugees following the Soviet repression. They were resettled across 37 countries, with most going to Austria. The international relief organization CARE provided welcome kits, and the U.S. Department of Agriculture worked with CARE to ship more than 500,000 packages to Vienna for distribution by the Red Cross.
The Blood in the Water match was a water polo semi-final at the 1956 Melbourne Summer Olympics between Soviet and Hungarian teams on the 6th of December 1956. The match was extremely violent and was halted in the final minute to stop fighting among spectators. Hungary won 4-0 and was later awarded the Olympic gold medal. Spain, the Netherlands, and Switzerland boycotted the Melbourne Games in protest at the Soviet handling of the Hungarian uprising.