Hello, and thank you for this thoughtful and well-worded question! I'm unfortunately not an expert on the Chinese Civil War, but I'll try my best to provide some background.

The very short answer to everything is that Mao Zedong and the Communists never had any intention to cooperate with the Nationalists or the Americans in the long term. Before George Marshall even set foot in China, the CCP created plans to "neutralize the United States" or, as Zhou Enlai later expressed, "[make] use of the United States... [and] make every effort to delay the onset of civil war." Their position is quite understandable, of course: the United States wanted China under a non-communist government, and its policies consistently favored the Nationalists. Chiang Kai-shek, on his part, was initially amenable to negotiations, if only to pacify both the United States and the Soviet Union, even though his advisers warned that Mao would simply exploit the opportunity to consolidate his forces and that the United States would likely blame the Nationalists for any failure to maintain peace.

The Soviet Union played a major role in these developments, as you suggested. When the Red Army occupied Manchuria in August 1945 near the end of the Second World War, they handed over an enormous quantity of captured weapons and other materiel to the CCP: according to one source, "700,000 rifles, 1100 light machine guns, 3000 heavy machine guns, 1800 cannons, 2500 mortars, 700 tanks, 800 ammunition depots, and ordnance factories kept by the former Japanese Kwantung Army." The Politburo then recommended to the CCP a month later that they adopt the strategy of "expanding toward the north and defending toward the south"--that is, secure their position in Manchuria--to which Mao wholeheartedly agreed. In the meantime, while the Red Army allowed the CCP to maneuver freely throughout the region, they prevented Nationalist officials and troops from expanding their foothold. The Soviets finally agreed to withdraw after Chiang protested, but they delayed it until March 1946. This, along with the temporary ceasefire with the Nationalists later brokered by Marshall, bought extra time for Mao.

So the Marshall Mission never really stood a chance. Marshall himself failed to resolve the fundamental differences dividing the Communists and Nationalists (and I don't see how he could have); on the other hand, while he later reported that "almost complete, overwhelming suspicion" between the two parties limited any meaningful chance for mediation, Marshall also complained about the CCP's "unwillingness to make a fair compromise." You might consider this the "final straw," though Truman recalled him in January 1947 so he could serve as Secretary of State (allegedly without Marshall's prior knowledge). As for the military dimension, I'll defer to someone better-versed on the topic. I hope you find this helpful nonetheless! :D