Short answers, pulled from the story.
The Roman amphitheatre consists of three main parts: the cavea, the arena, and the vomitorium. The seating area is called the cavea which means enclosure in Latin. Arched entrances at both arena level and within the cavea were termed vomitoria to enable rapid dispersal of large crowds after events concluded.
Jean-Claude Golvin identifies earliest known stone amphitheatres in Campania at Capua, Cumae and Liternum. Such venues were built towards the end of the second century BC. Earlier stone amphitheatres known as spectacula or amphitheatra have been found despite claims about wooden origins.
Imperial amphitheatres comfortably accommodated 40,000 to 60,000 spectators or up to 100,000 in largest venues. They featured multistoried arcaded façades elaborately decorated with marble and stucco cladding. Most amphitheatres remained concentrated in Latin-speaking Western half as Empire grew.
Gladiatorial munera began to disappear from public life during 3rd century due to economic pressure and philosophical disapproval. Opposition came from increasingly predominant new religion of Christianity whose adherents considered such games an abomination. Last construction recorded in 523 in Pavia under Theodoric.
The Flavian Amphitheatre in Rome known as Colosseum remains largest amphitheatre ever built. Built from 72 to 80 AD it stands as icon of ancient Rome with dimensions 188 by 156 meters. Arena measured 86 by 54 meters commissioned by Emperor Vespasian but completed opened until 80 AD by son Titus.