yes, need to show you entered on dependant visa to apply for HKID. if you enter on a visitor visa (you can apply for dependant visa while on visitor visa), you will have to exit and come back in because the immigration needs to see the expiration date for the dependant/work visa. They can only put the expiration date when you enter because it is good for 1 year after you enter (the first year anyways, i hear that it is 2 years afterwards). oh, you can apply for HK visa while you are in HK on visior visa.
can apply for both work and dependant visa at the same time. this way you can get it at the same time. the agency should be applying for both of you unless his company doesn't want to pay for your visa fees. the dependant visa application is part of the work visa application. no reason to apply seperately except for agency cost. you can look up the application form: ID990A.
website for application downloads:
http://www.immd.gov.hk/ehtml/evfhk.htm
i think you are cutting it close if you haven't started yet. but having a HKID does help with cost. From what i understand, you will only have to pay HKD 100 per hospital stay and doctor visit for you and HKD 50 per day for your baby. Everything else is free. my colleague went from preparing to pay HKD 70,000 to only paying HKD 600 because they went into labor early (premature) and were redirected to QMH by their private hospital.
I know about what you mean about china not being good for babies. I feel the same way.
Also, for a public hospital, impossible they don't have room in public area unless they have reserved it for local HK woman. The price quoted to you also doesn't seem right. HKD 39,000 is the minimum fixed price for private hospitals. As i said in my first post, The public hospitals will take you in no matter what if you are already in labor, just have to pay HKD 49,000 instead.
I think being born in HK and getting hk visa (no HKID for children under 11, unless applying for HK passport) is the same if your child was born in China or HK. Still need to get a passport from your embassy first. From my understanding only Chinese citizens and HK permanent residents can have automatic ROA in HK (maybe another expat with experiance can provide more info). For you and your husband (I am guessing your husband is not a chinese citizen), the only difference is that your child will already be in HK when s/he is born.