(1) Public hospitals in HKG are very good. My eldest daughter was born at the Prince of Wales in Sha tin. We went privately however, for reasons that I will not delve into here,. The only difference between public and private, apart from a large bill is (or was) that the father is not allowed to be present at the birth if you go public. In our case my wife had a caeserean and I didn't fancy being there anyway.
regarding the food, if you are not keen on the local hospital food you can always get the family and friends to bring you in a subway and starbucks!
(2) Citizenship, at least one or the parents has to be a 'permanent' ID card holder and then the words 'established' are entered into the birth certificate, in which case the child will also get the 'permanent' ID card, however they will need to visit HKG at least once every 3 years to keep it.
(3) Since the handover in 1997, I don't believe any 'right of abode' to non-ethnic chinese is given anymore. i.e. the 3 stars on the back of the HK ID card. However, with a permanent ID card you have the 'right to land', unless it has all changed !