Short answers, pulled from the story.
The traditional date for Rome's foundation is 753 BC, though this remains a point of myth and uncertainty rather than historical fact. Ancient authors wove together stories of Latinus, Evander of Pallantium, and the Trojan hero Aeneas to explain how the city began.
By the late 3rd century BC, about a third of the people in Italy south of the Po river had been made Roman citizens through mechanisms like military service or direct government grants. These new citizens were liable for military service while others became allies frequently called on to join Roman wars.
In 49 BC, citizenship rights extended to the people of Cisalpine Gaul through Julius Caesar's decree. The number of Romans increased rapidly through further extensions over subsequent centuries until Emperor Caracalla issued the Antonine Constitution in AD 212 which granted citizenship rights to all free inhabitants of the empire.
Phenotype-related stereotypes certainly existed yet inherited physical characteristics typically held no relevance to social status. People who looked different from the typical Mediterranean populace faced no exclusion from any profession and records show no stigmas or biases against mixed-race relationships within Roman society.
Throughout late antiquity, Romanness became increasingly defined by Christian faith which eventually became the standard after Church leaders such as Ambrose launched formal assaults on paganism. Emperors and courts were viewed as Romans par excellence once Christianity gained imperial adoption during the period when power slipped from pagan hands.
Eastern Mediterranean populations under Byzantine control retained Roman as their predominant identity throughout centuries after the 5th century with emperor ruling from Constantinople known as New Rome. By the late 7th century, Greek began being referred to as rhomaisti meaning Roman way of speaking and late 11th century references describe people as Rhōmaîos by birth signaling completion of transformation into ethnic description.