Nudity rule requires branding the slave (actually I believe it requires branding them twice, to fully upgrade to advanced-branding).
As for birthing, if someone has a baby then you get a new slave. That's all the consequence there is. That said, it is a little more complex then that. There are requirements and costs associated with giving birth. If you do not meet the requirements or wish to pay the cost then you do not get the slave and life continues on. Also, there is some recuperation time for a mother.