Can't help with number 1) but seems like this might be asking a bit much.
2) , bring your own, they will not be provided.
3) Have TA ask for this when booking. If you don't get it , ask Maitre D. If he can't help, eat in alternative dining areas.
4) If the baby is asleep or not crying , why not bring her to the show? If she is crying or fussing, perhaps one of you could enjoy the show .
5) Medical services onboard are extra charge. Get travel insurance. Do not expect a qualified pediatrician onboard and if this is an issue with you then cruise travel with an infant might not be a good vacation. Expect only very basic medical services to be available shipboard and even on land depending on ports of call.