What have China and the U.S. learned from each other in the Korean War?

After the U.S.-led forces were driven back to the south half of the Korean peninsular and had to sign a ceasefire agreement with China, I believe that some people must be quite surprised that after so many humiliating military defeats suffered by China the Communists actually forced U.S. and its small brothers to a negotiating table for some kind of ceasefire agreement with a country they had invaded, robbed, raped, humiliated and exploited since 1840. The lesson for Americans and their fellow invaders has been clear: a New China had come into existence and think twice before taking on China again. Of course, China also learned that U.S. is not a country to be trifled with. This is a two-street scenario. But, if either side wants to live through it all over again, U.S. and China will be in for another ceasefire agreement in the days of nuclear winter, if the two countries are still there in the new winter at all! I believe this is a nightmare both sides (China vs. U.S./its Allies) try to avoid. China has the will to keep Taiwan within its territory. But, does the U.S. have the will to fight China on behalf of pro-I Taiwanese for an island the People's Republic of China (1949- ) inherited from the Republic of China (1911-1949) that inherited from the Qing Dynasty (1644-1911)? I doubt it. Because this time, it is China with 1.3 billion people, the bombs, satellites, spaceships, warheads, etc. Most important, with the support of its people.