In terms of bags, whatever rule applies for your international leg applies for the domestic as well. thus, if you are allowed 2 bags from SFO - HKG - BOM, the same will be allowed in BOM - HYD as well if you book the entire strech as a single ticket.
in terms of connection time, a couple of hours should be sufficient. I've had closer connections (40 mins) 3 times in Bangalore and still made it without losing a single check-in bag. BOM airport may not be that efficient.

if you want to have a better flying experience (i.e. comfort, nicer stewardess, better food etc..), I would suggest other options like emirates / BA/ singapore airlines