The umbilical cord one I can answer because when I was pregnant I asked this and was told no. when a baby is born usually but not always the baby hasnt taken their first breath and scream yet. That usually comes after the cord has been cut and the baby is turned upside down to help drain its lungs of amniotic fluid if any got in the airway. then the baby screams because they got their butt popped or thier toe pinced to make them cry to help with the circulation and fully inflate the lungs. If the baby felt the cutting of the cord there most likey would be a scream like none other. Also though the umbilical cord contains lots of cord cells and red blood cells and so on there is not nerves or nerve endings inside to it.