When did China colonize Korea and Vietnam?

Answer 1

China did not colonize either. Colonization implies a movement of your population and control into what was previously territory that did not have your population or was not under your control. China established a system of vassalage, where any state near to China would come under its strong influence as a tributary state and would receive Chinese protection from "Barbarians" in return. Korea was a "good" vassal and remained in the Chinese sphere without problems from the 1300s until the late 1800s. Vietnam was a "bad" vassal and so they periodically revolted against the Chinese. Therefore Vietnam was a Chinese vassal intermittently (more off than on) ever since the year 1010 until the French colonization in the mid-1800s.