Yes, China can move forces into Burma/Hong Kong before UK is at war with Japan.
You are right, it is UK/ANZ that cannot move over or into China at all without a DOW on Japan, but China can move into Burma/Hong Kong before Japan and UK are at war with each other.
China IS an ally with UK at game start because UK is at war with G/I and China is at war with J, and J and G/I are allies.
No, this movement to Hong Kong or Burma by China is not a provocation for Japan. ONLY UK/ANZ can “provoke” Japan, and this ALWAYS comes in the form of a DOW by UK/ANZ on Japan.
Russia has to be at war with Japan before Russia can move anything into China. I think that’s what you’re missing.
So Russia is an allied power as of R1, although only on the Pacific map.
Japan can DOW Russia any time and Russia can DOW Japan any time. No action by Russia can ever be considered provocation that allows J to declare war on UK/ANZ without bringing USA in. Provocation only comes from UK/ANZ, and would always come in the form of a DOW by UK/ANZ on Japan. A DOW is required by UK/ANZ to fly over anything Chinese or move anything into China.