Short answers, pulled from the story.
The Italian Communist Party was founded on the 21st of January 1921 in Livorno, when a faction led by Amadeo Bordiga, Antonio Gramsci, and Nicola Bombacci split from the Italian Socialist Party. It was initially named the Communist Party of Italy before being renamed the Italian Communist Party on the 15th of May 1943.
The PCI reached its highest ever vote share in the 1976 Italian general election, winning 34.4% of the vote, equivalent to 12.6 million votes. At that time it was the largest communist party in any capitalist state.
The PCI was expelled from the Italian cabinet on the 31st of May 1947 under pressure from the United States. Secretary of State George Marshall told Prime Minister Alcide De Gasperi that anti-communism was a precondition for receiving American aid, and Ambassador James Clement Dunn directly asked De Gasperi to remove the PCI from government.
The Historic Compromise was a policy pursued by PCI secretary general Enrico Berlinguer, seeking cooperation between the communists, Christian Democrats, and Socialists through democratic means. The kidnapping and murder of DC leader Aldo Moro by the Red Brigades in May 1978 effectively ended prospects for the compromise, and it was formally abandoned as party policy in 1981.
The PCI held Bologna continuously from 1945 onward and used it as a model of clean, uncorrupt local administration. Between 1946 and 1956, the communist city council built 31 nursery schools, 896 flats, and 9 schools, and provided subsidised school meals to 8,000 children. In 1972, Mayor Renato Zangheri introduced an innovative traffic plan restricting private vehicles and investing in cheap public transport.
General secretary Achille Occhetto, who took office in 1988, announced the party's transformation at a 1989 conference in Bologna's Bolognina district, citing the collapse of communist governments in Eastern Europe. The party dissolved and refounded itself as the Democratic Party of the Left. A third of its membership, led by Armando Cossutta, refused to join and instead formed the Communist Refoundation Party.