Short answers, pulled from the story.
Imre Nagy was a Hungarian communist politician who served as de facto Prime Minister twice, in 1953-1955 and again in 1956. He led the Hungarian Revolution of 1956, announced Hungary's withdrawal from the Warsaw Pact, and was executed by hanging in June 1958 after a secret trial. His reburial in 1989 drew an estimated two hundred thousand people and played a key role in the collapse of communist rule in Hungary.
Imre Nagy was executed by hanging on the 16th of June 1958. He was secretly tried by János Kádár's government and found guilty of organising the overthrow of the Hungarian People's Republic and of treason. His trial and execution were made public only after the sentence had been carried out.
Imre Nagy was reinstated as Prime Minister on the 24th of October 1956 as a central demand of the revolutionaries. During the revolution he dissolved the ÁVH secret police, negotiated a ceasefire on the 28th of October, admitted non-communist politicians to the government, and on the 1st of November announced Hungary's withdrawal from the Warsaw Pact. After the Soviet invasion on the 4th of November, he fled to the Yugoslav Embassy.
Yes. Under the codename "Volodia", Imre Nagy served as an informer for the Soviet NKVD secret police from 1933 to 1941. The NKVD described him as a "qualified agent, who shows great initiative and an ability to approach people." His service as an informer was later cited as a factor in the Soviet support he received after World War II.
Nagy was initially buried face-down in the prison yard where he was executed, with his hands and feet bound with barbed wire. He was later moved to section 301 of the New Public Cemetery in Budapest. In 1989, on the 31st anniversary of his execution, his remains were reburied with full honours in the same plot.
A popular statue of Imre Nagy inaugurated in 1996 was removed from its central Budapest location on the 28th of December 2018. The stated reason was to make way for a reconstructed memorial to victims of the 1919 Red Terror. Opposition parties accused Viktor Orbán's government of historical revisionism in connection with the removal.