This is an excellent article on Childhood in the Middle Ages, though not specific to the care of babies.
https://www.medievalists.net/2018/11/childhood-middle-ages/
There are also a number of good books on childhood in the Middle Ages, aside from the regular descriptions of the so-called "Child's Crusade" of 1212, which unfortunately resulted in many of the children being sold into slavery in North Africa rather than taken by ship to the Holy Land.
The best source I have found for specifics on children in the Middle Ages, (which you'll want to get from your library) is Childhood in the Middle Ages, by Shulamith Shahar, which goes into great detail on each social class's care and treatment of children from birth to adulthood.
I'm sorry I can't go into more detail to answer your specific questions as it is not my specialty (that is working women in the same time period), but Ms. Shahar's book covers everything you asked.