1) Keep in mind that these are global companies, as such, these policies are not exactly “Local” policies, They’re essentially the same as outside China, except that they are approved to be sold within China in accordance to CIRC regulation. They allow the same access worldwide (within area of cover, i.e. world-wide excluding USA) and as such, you can get treatment wherever you wish to get treatment.
In fact, with healthcare costs being what they are in China, if it makes sense financially or if there is no adequate medical facility locally, they will actually fly you somewhere else to be treated. In this case, only the transportation costs would need to be approved.
2) They are, usually all the major private hospitals will have this kind of agreement.
3) Claims handling with these international insurers is not really a problem, there are some insurers that have some growing pains when first entering China but a good broker should know who they are and stay away from them until they have everything in order.
4) Again, you can seek treatment wherever you want.
The main difference with these “local” policies is that they are licensed to be sold in China, that means that you get a Fapiao and that it is regulated by CIRC (China’s regulatory body).
Hope this answers your questions.