Is passing aids from an infected mother to her baby avoidable, either before or after birth?

Yes. Current therapies which cut down the active HIV viral load during pregnancy has led to a reduction of maternal/child passage to below 5%.Baby is usually put on meds soon after birth until a variety of tests confirm the kid is clear at which point they are stopped, or continued if there is any evidence of the illness. Breastfeeding is not advised because it could transmit the germ.
Yes. With treatment prenatally; during labor and delivery & treatment of the newborn transmission can be prevented.