Short answers, pulled from the story.
Varro and Plutarch settled on 754/53 BC claiming the 21st of April 753 BC synchronized with an eclipse. This date became the official chronology used from Claudius's Secular Games in AD47 to Hadrian's Romaea in AD121.
Current evidence suggests there were three separate bronze-using settlements on the Capitoline during the period 1700 to 1350 BC. Core samples show that the terrain of Bronze-Age Rome differed greatly from what is present now, including a seasonally dry plain north of the Aventine Hill.
Romulus and Remus are the grandsons of Numitor, the king of Alba Longa. They were suckled by a she-wolf at the Lupercal cave before being discovered by the shepherd Faustulus and his wife Acca Larentia.
Four major settlements emerged in Rome with nuclei appearing on the Palatine, the Capitoline, the Quirinal and Viminal, and the Caelian, Oppian, and Velia. The area north of the Aventine Hill was a seasonally dry plain that provided a safe inland port for seafaring ships.
The first attempts to tie this story to Rome were in works of two Greek historians at the end of the fifth century BC. Hellanicus of Lesbos and Damastes of Sigeum likely only mentioned off hand the possibility of a Roman connection before more assured connections emerged at the end of the fourth century BC.