Outer Mongolia gained independence because of Russian and later Soviet involvement. Plain and simple. Sure, some Mongolians were involved, but the fact stands that without Russian/Soviet involvement, Mongolia would not have been independent. The issue is not just about lands that were lost, the Russians/Soviets also caused mass suffering and deaths in inner Manchuria. From the Russo-Japanese War to the Warlord Era to the "Liberation" at the end of WW2, countless Chinese suffered/died due to Russian/Soviet actions. But as Imperial Russia, the Soviet Union, and Qing China all no longer exist, history shouldn't preclude cooperation between the Russian Federation and the PRC. But neither should history be whitewashed/forgotten just because of the current strategic partnership. The history of the Century of Humiliation should never be forgotten, and Chinese are pragmatic and intelligent enough to both remember the real history and see the importance of a mutually beneficial partnership with the Russian Federation.
The carrier, as well as the Su-33 prototype which aided the development of the J-15 came from Ukraine. Also, Ukrainians provided massive assistance to the Chinese aerospace and space industries. By that logic, should China be siding with the Ukrainians? The USSR helped China for a short period of time from 1949-1962 when the interests of the two countries aligned. The Germans also helped China for a decade prior to WW2 and the West helped China for about a decade towards the end of the Cold War, also because interests aligned. China doesn't owe anything to any of those nations/blocs.
Imperial Japan could never have won. By the time the USSR pillaged liberated Manchuria from the emaciated remains of the Kwantung army in 1949, Japan was losing ground in all fronts across China and the Nationalists were already planning their final offensive. More than 20 million Chinese also died during WW2. The Soviet sacrifices were for the survival of their own nation, against the Germans, nothing to do with China's war against Japan. The US/UK contributed far more in the fight against Japan than the USSR ever did, and even their contribution is only a drop in the bucket when compared to the Chinese war effort. If the USSR didn't exist, there would not have been a Korean war in the first place. The USSR had an equal stake as China in the Korean war, yet it was only Chinese that paid in blood.
No. Historically, China suffered far more than benefited from Russia. China should support Russia because partnership today benefits both countries. Specifically, China should support Russia because supporting Russia is good for China. Past history (both the good and the bad) should have no impact whatsoever on the strategic calculus. Sino-Russian partnership has the potential to be mutually beneficial for a long period of time, and it would be in China's interest to focus on building lasting ties that will persist far into the future. But there should be no illusion of any form of, "forever brotherhood," and China should hedge against a divergence of interests between Russia and China. Again, the Sino-Soviet friendship lasted barely a decade before the PRC and USSR became strategic adversaries.