How much does it cost for the Broken Lords empires to purchase each population unit?
I know this is related to both total population and the population at the current city. Are there any other factors? Are there ways to reduce the cost?
It is hard to give you an exact cost as it varies. Indeed it is related to the total population of your empire, not just the city.
There are no ways to reduce the cost.
(Right now it seems there is a general feeling that the cost might be too steep and it might be reduced in future patches, so the values will probably change.)