Short answers, pulled from the story.
Archaeological evidence of settlement around Rome starts to emerge in the middle of the 8th century BC. Large-scale organisation appears only then, with the first graves in the Esquiline Hill's necropolis.
The Romans themselves had a founding myth attributing their city to Romulus and Remus. These sons were offspring of Mars and a princess of the mythical city of Alba Longa.
The later Roman antiquarian Marcus Terentius Varro placed the city's foundation to 753 BC. The story dates at least to the 3rd century BC.
On the 16th of July 390 BC, a Gallic army under the leadership of tribal chieftain Brennus defeated the Romans at the Battle of the Allia. The Gauls looted and burned the city then laid siege to the Capitoline Hill for seven months.
Hannibal's invasion lasted over 16 years ravaging Italy but ultimately Carthage was defeated in the decisive Battle of Zama in October 202 BC.
In 284 AD Diocletian was hailed as Imperator by the eastern army. A new form of government was established called the Tetrarchy.