Uruk was build in 5000 BC by the Sumerians. In the Bronze Age it was the center of civilization but would be displaced by Babylon in that role later. A plenty of Sumerian words were taken up into the Akkadian language and I've still encountered some of them in the etymological dictionaries of Hebrew and of Arabic. Presumably you can expect to find some more in those of Greek and Persian as well. In 700 AD Uruk was abandoned because it no longer was a gleaming metropolis but a desert with some fancy ruins.
Did the flow of the Euphrates change around the time of Sumerian decline?
The final decline of Uruk and the decline of independent Sumer are separated by about 2700 years and thus cannot be too closely linked. The final independent and powerful Sumerian dynasty was the Third Dynasty of Ur (centered in Ur) from 2100-1950 BCE. The cities of Uruk and Ur and indeed many other Sumerian cities survived and flourished well beyond the fall of Ur III and eventually were abandoned for a myriad of reasons of which the shifting of the Euphrates could be one. However I cannot really speak to the rise and decline of urban areas in Mesopotamian Antiquity as it's a bit out of my area of study.
As for Ur III's fall it was likely caused by a combination of the increasing salinization of agricultural land, the incursions of pastoralists (Amorites) and an Elamite invasion rather than any shifts to the Euphrates river. In fact I am unaware of any major shifts in the river's course during this period.
However though the shifting of the Euphrates was not a factor in the decline of Ur III the constantly moving waterways of southern Mesopotamia may have had major impacts upon the urbanization process of the Early Dynastic period (2900-2500 BCE). It has been posited that the instability of the waterways led people to abandon smaller rural settlements and instead congregate in large and stable urban areas such as Uruk thus shaping the development of greater Sumer immensely.
There is a dynasty that was ended by a king who redirected the flow of the river to quell unrest and then couldn't put it back. I believe this was isin, though. I would have to look it up to be certain.
