Can anorexia when the mother is pregnant hurt the baby?

Yes. Both mom and baby need a lot of calories during the pregnancy (about 400 more calories per day for a normal weight woman). Not eating enough during pregnancy can ultimately hurt the baby, although the mom will start to see symptoms before the baby will (the baby's metabolic needs will take precedence).
Yes. Anorexia can cause a variety of physical problems which could have a negative impact on both the mother's and baby's health.
Yes! Your baby needs nutrients to grow and thrive in the womb. An anorexic mother needs to haver her mental state carefully monitored during pregnancy, and there is risk to her going off antidepressants during pregnancy. Counseling and mental health support are critical!