In general, no, Mesopotamia did not fall because of attack from other empires, since it was primarily due to the Tigris and Euphrates Rivers drying up that led to a lack of produce, and therefore a fall in the empire itself.
first here's the definition of a Proxy War : A proxy war is an armed conflict between two states which act or on behalf of other parties that are not directly involved in the hostilities. so the US government aided Africa even though they were not directly involved in the war themselves.
