Why are you moving to Japan? Is this related to a company? Work? Education? A lot of times they have some sort of system to assist with moving into an apartment or residence in Japan.
How long will you be here is another very important bit of information.
Either way, start learning Japanese. NOW. I recommend the genki series of books. This website also has good information.
AJATT | All Japanese All The Time | You don't know a language, you live it. You don't learn a language, you get used to it.
Browsing this forum or Japanese cultural sites can give you some very basic information. It's certainly not going to replace experience or teach you everything, but it is a critical base and foundation that you must have to start somewhere.
As for schools, I know of friends who have been able to jump into Japanese schools, but since they are taught in Japanese, most kids are very lost, even if they DO try to accommodate. I believe there are international schools taught in English but I personally know almost nothing about this. Another member might.
There are various venues and areas where you can continue the activities you are mentioning, but of course many will require at least some Japanese language ability to begin interaction with. No matter how limited you might be, you have to push for as much language ability as you can during your prior time and arrive. It truly is critical.
As for your child on the way, I don't think you have anything to worry about in terms of quality of care, and there are English speaking doctors as well in some areas here. Again, other members might have more detailed information. You'll be covered by national health insurance so you will have coverage (however babies still cost money to give birth too) but I believe international doctors are not covered by such insurance sometimes.