Latin obviously was the language of the elite but did the plebeians and slaves outside of Italy adopt Latin? Would the lower classes speak Latin in places like Gaul, Iberia, Britain, or Carthage?
Also, did the Romans ever try to replace Greek with Latin in their eastern provinces?
Ordinary people in western provinces in Gaul and Iberia started to speak Latin in the 3rd century. This might have to do with structural changes in the Roman empire such as decentralization of government, enhanced social mobility due to military gaining importance.