The baby's entire circulatory system does not start working independently until after the birth, when the lungs receive oxygen.

However, your child's heart is already ready and has almost reached its final form. Its immune system is now working fully independently. Nevertheless, after the birth, it will still take some time until the baby can protect itself from infections. It must first form sufficient antibodies of its own to do so.

The baby is occupying the entire abdomen and pressing your lungs together. This can cause you to experience shortness of breath. The uterus is also pressing against your ribs, which can be painful. The false labour pains are probably becoming more frequent and allowing the baby's head to sink deeper and deeper into the small pelvis. In this way, your baby is assuming the birthing position. This has a positive side effect for you as you will suddenly be able to breathe better and any heartburn will also now abate.

If you have given birth before, your uterus will probably not drop until just before childbirth. 

During weeks 33-37 of pregnancy your baby is about the size of a honeydew melon.

Baby Entwicklung Schwangerschaftswoche Honigmelone 19