I am not sure how old are you, but if you are a single and young female would like to entry UK is not that easy for just having a tourist status.
Try to answer your questions
1. NHS is for UK citizens, or if you have a valid visa (etc: student visa), you are also entitled to enjoy this benefit. If just tourist, I dont think you will be entitled to enjoy the FREE services
2. If your baby is born in UK, the baby should be a British citizen. better check with Home office website. For the HK side, please check with HK Immigration office.
3. UK Dependent visa - you must apply it in your home country (British Consulate), not apply in UK. Once approved, you will have to stay in UK for certain years before you become British citizen. Before that you will have to take a test including UK culture and your english standard.
4. If your child born in HK, then both of you will have to apply dependent visa.
I am not sure the cost, but tbh, the living cost is higher in UK.