China did not support North Korea's invasion. North Korea did not seek China's support initially and only asked for Stalin's permission. China would not have entered the Korea war at all if MacArthur did not disobey Truman and marched all the way to the Chinese border. He also publicly stated that he planned to bomb China. It was one of the reasons for which he was fired. All this was well documented in the US's own literature.
I don't see how to read China's dispatch of 1.5M combat troops, taking on some 110,000 battle deaths (thus saving the invasion from imminent collapse) other than as "support" for the invasion.
I don't see any substance the point you're trying to make here. One could try to say, "China was only trying to preserve North Korea's borders prior to the invasion". But once it pushed further south, into South Korea proper -- it was joining the invasion. There's nothing to debate here.
1) to make sure China was not invaded as MacArthur intended
And this just makes no sense at all.
MacArthur never intended to invade China, and didn't even start making noises about bombing China until after the it joined the war effort.
Vietnam, 1979.
Support for North Korea's invasion of South Korea 1950-1953.
Invasion of Indian-held areas in 1962 based on extremely dubious claims.
Not an invasion, but its support for the genocidal Khmer Rouge in the 1970s (who ended up invading Vietnam with Chinese arms) was quite significant.
Its current menacing of the Phillipines.
Claims about "traditional borders" are almost invariably nonsense.