First: is there a difference when a civilization "Decreases" it's population and when a civilization "Loses" one of it's population?
No, the effect is the same: You put one yellow stone back to your yellow bank (either from your unused workers or from a technology).
Another thing is the loss of a yellow stone (that goes from your yellow bank back to the box) or the destruction of a building (that goes from a technology to your unused workers).
Second: What happens when there is a tie in a war?
Nothing. A War's effect is based on the strength difference, and in case of a tie the strength difference is zero, so nothing happens.