Short answers, pulled from the story.
The Roman province of Mesopotamia was organized in early 116 when coins were minted to celebrate the achievement. This followed the conquest of northern Mesopotamia at the end of 115 and the subsequent march into central and southern regions later that same year.
Emperor Septimius Severus re-established a province of Mesopotamia in 198 following his successful war against Parthia. He elevated Nisibis to the status of a full colonia and made it the capital of this new territory.
Nisibis and Singara were lost after Julian's Persian expedition in 363, causing the capital to transfer to Amida while the seat of military commander dux Mesopotamiae moved to Constantina. Other cities included Martyropolis and Kephas within the administrative structure of the Diocese of the East.
The entire region was lost permanently to Muslim conquests between 633 and 640 after being regained following the great war between 602 and 628. Control had been fought over between Roman and Sassanian empires until these final losses occurred.
This new territory was limited between Osroene to the south and the Euphrates and Tigris rivers to the north. The river Chaboras marked the eastern boundary of the province.