Short answers, pulled from the story.
The Capitoline Museums trace their origins to 1471, when Pope Sixtus IV donated a group of ancient bronzes to the Roman people. Pope Clement XII opened them to the public in 1734, making them among the earliest museums in the world accessible to all citizens.
The Capitoline Wolf is a bronze sculpture long believed to be an Etruscan work from the 5th century BC, though some restorers have proposed it may date to the 12th century. The twin figures of Romulus and Remus were added in the 15th century and attributed to Antonio del Pollaiolo. It is held in the Capitoline Museums on the Capitoline Hill in Rome.
Michelangelo Buonarroti designed the Piazza del Campidoglio at the commission of Pope Paul III. The project was undertaken for the occasion of Emperor Charles V's visit to Rome and included renovation of the Palazzo Senatorio, a new facade for the Palazzo dei Conservatori, and the construction of the Palazzo Nuovo.
The Treaties of Rome, which established the European Economic Community, were signed in the Hall of the Horatii and Curiatii inside the Palazzo dei Conservatori in 1957. The six signing nations were Belgium, France, West Germany, Italy, Luxembourg, and the Netherlands.
The Dying Gaul is a 3rd-century Roman copy of a Greek bronze original from the 3rd century BC, part of a triumphal monument commissioned by Attalus I to celebrate his victory over the Galatians. It was purchased for the Capitoline collection in 1734 and became perhaps the most famous work in the museums, replicated many times in engravings and drawings.
The Centrale Montemartini is a former thermoelectric power station in Rome's Ostiense district that became a permanent branch of the Capitoline Museums in 1997. It houses a permanent collection of 400 ancient sculptures, many excavated from Rome's ancient gardens between the 1890s and 1930s.