Short answers, pulled from the story.
The borders of the Roman Empire combined military roads and linked forts, natural frontiers such as the Rhine and Danube rivers, and man-made fortifications. In some provinces a continuous wall was built; in others such as Syria and Arabia Petraea, a net of border settlements and forts served instead.
The Roman Empire may have reached its greatest territorial extent under Septimius Severus, encompassing two million square miles of territory.
Hadrian's Wall was a defensive fortification constructed in 122 to protect the province of Britannia from the Caledonians, holding a garrison of fifty thousand soldiers. It was one of two walls the Romans built in Britain; the second, the Antonine Wall, was constructed between 142 and 144.
In classical Latin, limes had several meanings, including a path, a boundary line, any road or path, a channel, or a distinction between two things. After the third century it became an administrative term for a military district commanded by a dux limitis. Modern scholars use it as a general term for the Roman frontier, a usage the Romans themselves never adopted.
Along its eastern borders, the Roman Empire faced the Parthian Empire and then the Sasanian Empire, which succeeded the Parthians in 224-226. The Sasanians were recognized as a leading world power alongside Rome and the Byzantine Empire for more than four hundred years.
The Roman Empire controlled the North African coast from the Atlantic Ocean to Egypt, with the Sahara and the deserts of Arabia forming the southern natural barrier. Along the Nile, Roman control extended to Qasr Ibrim, the southernmost point of the empire, near the modern border between Egypt and Sudan.