Would a woman with a heart transplanted be able to survive pregnancy and childbirth?

Hard to say. This would best be a question for the individuals treatment team. Each case is unique. The woman may need to be on medications that could cause fetal anomalies or otherwise interfere with fetal growth & development. Without having all related information in hand it is not realistic to generalize an answer.
Possible. A number of women with transplants have born children. In this case the questions to answer are; how close a match and how much of what anti-rejection meds are used? What is the cardiac status of he transplanted heart, "how well is it working"? A long discussion with the transplant doctors is in order.