I've done thousands of weather deviations in the PRC, I've never had to climb or descend in order to facilitate a deviation, nor have I heard of it occurring. I think that would be an extraordinary occurrence. However nothing surprises me anymore, so it is certainly possible!
Deviating while crossing an FIR boundary is generally not a problem. The controller usually coordinates it with the next sector. Of course, once in the new sector if you want to do something different from what you have been doing then you would have to advise them of your new requirements. Same as operating in the West. As I wrote above, on the rare occasions when you have a deviation refused and are unable to negotiate an alternative then declare a PAN and just do what you need to do. There will never be any comeback for doing this.
You will find that you are descended to lower levels not because of "what is filed on your flight plan", as The Loner suggests above. It is due to conflicting traffic or because there are often (usually non- negotiable) arrangements that traffic must cross boundaries or points at particular levels. For example, traffic down the east coast of China bound for Hong Kong or Macau are required to descend to cross IKATA (the Shanghai/Guangzhou FIR boundary) at 9800 metres. They specify a descent rate to minimise the exposure to traffic conflicts on a busy 2 way airway while an aircraft descends through multiple levels.