deirds I wouldnt think finding a gyn/obstetrician or a midwife should be much of a problem in Berlin. we moved to a small city so choice was limited, and the popular ones were not taking on any new patients. I was lucky though as I lived there as a child/teenager and was still on the patient records of one of the popular ones. Finding a Hebamme was slightly more difficult for me, but mainly because I was already so far gone. I am sure you'll be fine!
do you know if you want just the ''regular' Hebamme who will come and see you at home before and after the birth for check ups? or will you be looking for a Beleghebamme? they do the normal check ups, but will also come to hospital with you when you give birth. that way you have a midwife there with you who already knows you, and you know her.
I have to say, I still dont completely understand the insurance situation you describe. You say you partner's work will insure you? does that mean it will be private health insurance?? or have they simply chosen one of the state subsidised insurance providers (gesetzliche Krankenkasse) for him, so that he doesnt have to worry about that bit? If it's the latter, then find out which one it is an try to start your membership (and I would assume it would have to be for your partner and your son too) a month early. as neither of you are working, the type of membership will be called 'freiwillige Mitgliedschaft'. and as I mentioned before, the cost for the freiwillige Mitgliedschaft would be paid for by the Arbeitsamt if you decided to apply for Arbeitslosengeld 2 for that one month.
I really cant see an insurance provider taking you on for just one month....but apart from that, wouldnt it be much easier to start membership with the one you will be covered by from FEbruary anyway?
wrt to the question about whether YOU will be covered as well, as you are not married: f it is a gesetzliche Krankenkasse, then the answer is yes, you should be. you and your partner would be classed as having a 'eheähnliche Lebensgemeinschaft', especially with you having children together. if it is a private health insurance, then you probably would not be covered by it.
sorry for waffling, I'm just trying to understand the full situation 