It was more of an enemy of my enemy alliance. The West and the Soviet Union have hated each other from the start. The ideologies of the two are not meant to co-exist, Capitalism is everything that Communism and Socialism wants to bring down, so there was always rivalry. I'll try to answer, or expand on some of the points that you've made.
The Soviets and the US wished to expand their influence on Europe, in fear that the other will expand first. So there was a sort of race to Berlin to "liberate" it first. Both sides wished to increase their spheres of influence. It was all both defensive, neither side really wanted another major war, they were both mostly scared of the other attacking so they wished to gain more people for their sides army. Stalin wasn't too big on ideology, sure he was a Communist, but he was mostly a Stalinist, he loved himself, and wished to hold onto power. He cared more about holding power than spreading socialist revolution or being a true Communist or Socialist.
German Soldiers tried to escape to the US because those bastards, excuse my language, treated the Slavic population horrendously. Slavs and Jews were the two major populations targeted for extermination. Hitler's master plan was to take all of Eastern Europe and 1/5 of Russia, exterminate the population and colonize with German farmers, to be self sufficient. Nazi Soldiers were brutal, and terrifying to the local populaces, mass shootings, gassing (with gas vans), and in many cases rape were prevalent. They would put POW Soviet Soldiers in camp they were pretty much as deadly as death camps. Disease, starvation and shootings would take care of the Soviets for the Germans. So, you could understand that the Soviets were going to completely torture, and rape the Germans once they caught them, and for this reason the Germans ran towards Americans (who they treated relatively well).
I've actually never heard of that movement, do you mind giving me the name? It could be in the realm of truth, both sides despised Communist, and Bolshevism.
Russia only fought Japan for 2 weeks because Japan didn't declare war on the Soviet Union with Germany. Hitler asked them not to declare war actually. Soviet Union only declared war on Japan because the Allies needed some more help, and Stalin stated once Nazi Germany was defeated, they would help fight Japan. They helped a good amount, destroying Japanese Armies on mainland Asia and contributing to the defeat of the Japanese, although I believe the Atomic Bombs did more to cause their defeat.
Also, it wasn't just Russia who fought Nazi Germany, it was the Soviet Union. They were sort of a Pseudo-Ally, it was almost like there were two separate wars, The Soviet-Nazi War and the Western-Nazi War. Both sides didn't really like each other, and wished to make gains for themselves, but realized they needed each other to win.