Short answers, pulled from the story.
Armed conflict in the Chinese Civil War began on the 1st of August 1927 with the Communist Nanchang Uprising and concluded with the last organized Nationalist resistance collapsing on the 10th of December 1949. The war is divided into two main phases, with an interlude during the Second Sino-Japanese War from 1937 to 1945.
The alliance broke down because KMT leaders feared the Soviet-backed CCP was trying to infiltrate and destroy the Kuomintang from within. On the 12th of April 1927, General Bai Chongxi ordered mass arrests and executions of Communists in Shanghai, an event the CCP called the Shanghai massacre. Chiang Kai-shek denounced the left wing of his own party for taking orders from the Soviet Union over Sun Yat-sen's principles.
The Long March was a massive military retreat by Communist forces from their Jiangxi base area beginning in October 1934, covering what Mao estimated as 12,500 kilometers over roughly a year to escape KMT encirclement. Of the 90,000 to 100,000 people who set out, only around 7,000 to 8,000 reached Shaanxi. The march established Mao Zedong as the undisputed leader of the CCP, with Zhou Enlai and Deng Xiaoping as vice-chairmen of the Military Commission.
On the 12th of December 1936, Generals Zhang Xueliang and Yang Hucheng kidnapped Chiang Kai-shek to force him into a truce with the Communists. Both generals commanded forces that were supposed to be fighting the CCP but had secretly signed ceasefire agreements with them, frustrated that Chiang prioritized the civil war over resisting Japan. The incident resulted in the formation of the Second United Front, suspending the civil war.
Within less than two years after the end of the Sino-Japanese War, the KMT received $4.43 billion from the United States, most of it military aid. About 50,000 US soldiers were also sent to guard strategic sites in Hebei and Shandong under Operation Beleaguer. The US also airlifted KMT troops from central China to Manchuria to contest Communist control of the Northeast.
The Liaoshen Campaign (launched the 12th of September 1948), the Huaihai Campaign (late 1948 to early 1949), and the Pingjin Campaign (the 21st of November 1948 to the 31st of January 1949) were the three campaigns that broke KMT power. Together they destroyed 144 regular and 29 irregular KMT divisions, including 1.54 million veteran troops. The Huaihai Campaign was the largest single military operation of the entire war.