...(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)?
What we have is nothing. Yet with regards to China people talk about the 'invisible hand'. Invisible my ass..
How do they sell them off? Auctions do happen. What they look for is sometimes foreign partners who are willing to buy said factory and include it in their operations...
They also look for some locals who often get loans (aka banking crisis) and buy what are deemed non critical companies and try to hence manage them to profitability.