Short answers, pulled from the story.
The Roman people refers to the body of Roman citizens during the Roman Kingdom, the Roman Republic, and the Roman Empire, a status that expanded from Latins in Rome itself to nearly every subject of the empire in late antiquity.
Roman citizenship became close to universal in AD 212, when Emperor Caracalla issued the Antonine Constitution, extending citizenship rights to all free inhabitants of the empire.
Cicero and other Roman authors took pride in Rome's identity as a 'mongrel nation' because the city's founding myths, including Romulus's sanctuary and the mixing described by the historian Dionysius of Halicarnassus, portrayed Rome as built from migrants and fugitives rather than one bloodline.
Roman identity faded in most of Western Europe by the 8th and 9th centuries, but it survived continuously in Italy as the demonym for Rome's citizens and endured in the Byzantine Empire in the Greek-speaking east until the fall of Constantinople in 1453.
Under Vandal rule, the Roman-descended population of North Africa largely stopped identifying as Roman, instead calling themselves Libyans or Punic people, while the Vandal state promoted the legacy of Carthage.
The Romansh and Romands of Switzerland and the Romanians, Aromanians, and Istro-Romanians all derive their names from the Latin Romani, and Greeks used Romioi as a self-identity into the 20th century.