3. Your idea of control sounded right. It was your idea of “Chinese territory” that seemed to have the problem I think?
China can only spawn units in (1) Chinese territories (2) that it controls. If Calcutta falls, and China captures Kwangtung/Burma, they do absolutely control them (and gain the IPCs from them, and the (,in the case of China, limited) use of the facilities, and everything else control implies). That satisfies but one half of the requirement (2). They are not, however, Chinese territories–they are British territories. Only those territories with a Chinese emblem are Chinese territories, just as it is for every other nation in the game. Therefore one half of the above requirement (1) is not satisfied.
I hope that helps, and I’m not just misunderstanding you!
Edit-
Maybe if your A&A game lasted for 60-120+ turns, you could add a houserule that the British use of Hong Kong, which, in our now drastically different timeline, ended in 1997, takes effect, and Kwangtung is again a true Chinese territory… you know… just… a suggestion :p