The United States has never "conquered" China. Meaning that the United States has never occupied or taken over Chinese territory.
No.
The US will not support any country that it feels is fighting an unwarranted war.
The cast of The Men Who Would Conquer China - 2004 includes: Mart Bakal as himself
Mongolia
China
China
In 1279 Kublai Khan conquered all of China
China conquered Vietnam in 111 BC.
Italy or China
Kublai Khan ruled China but he did not conquer it; he inherited the throne from his grandfather, Genghis Khan.
Korea
Taiwan, Korea, And Northeastern china