Original sin is based on the belief that Adam and Eve are the parents of all mankind. Where and when did they live?

​The nature of your question asks the Genesis account to be what it really is not, namely, a scientific and strictly historical account of creation. It proposes to be neither of these. Rather it is more of a poetical account of God’s creative act. 
 
Hence the chronological dating of Adam and Eve to, say, 6,000 BC, based on Genesis is not possible. 
 
The account does seem to locate the Garden in Mesopotamia, but here too we need not presume this is meant as a precise map but could be more allegorical. 
 
What we must hold is that God created everything out of nothing and guided all the stages of creation, even unto this day. Catholic teaching does prefer to see Adam and Eve as directly created by God and as actual, historical persons.