The Columbia Encyclopedia, Sixth Edition slavery
References to it appear in the ancient Babylonian code of Hammurabi. Its form and nature varied greatly in ancient society. It seems to have been common in the Tigris-Euphrates civilizations and in ancient Persia.
1. The code of Hammurabi was as you said Babylonian, not Persian. Within the Persian Empire the local laws and costums remained largely in place. The Babylonian law would have continued in Babylon, but certainly not in all of the Empire. At least there is no reason to my knowledge to assume that.
2.
I am surprised why you trust an Islamist website for
historical source. They are the least someone would
trust on anything. I’m sure the Islamists have also a lot of things to say about Jews, Christians and the West.
I doubt you would agree with their views.