Demand in China is just that, demand that happens to be in China. Much of the 'internal demand' we are seeing is driven by multinational corporations or those companies servicing those multinationals.
...(b) Should the core SOEs be privatized and, if so, how?...
We don't even privatize everything here in the United States so no everything is feasible, I guess I'd like to see a specific list of industries before that question can be answered. Then it would have to be determined who would get to own the industry if privatized. How do you even do something like that? Hold an auction and sell the state's assets to the highest bidder(s)?