Short answers, pulled from the story.
The seven hills of Rome include Aventine Hill, Caelian Hill, Capitoline Hill, Esquiline Hill, Palatine Hill, Quirinal Hill, and Viminal Hill. These elevations form the geographical heart of the city within its ancient walls east of the river Tiber.
Romulus and Remus founded the original city on the Palatine Hill on the 21st of April 753 BC according to historical records. Small settlements occupied each of the seven hills separately before these groups bonded into a unified whole.
Vatican Hill lies northwest of the Tiber outside the boundaries while Pincian Hill sits to the north beyond the ancient limits. These four elevations fall outside the area marked by the Servian Wall and the pomerium so they do not count among the traditional Seven Hills.
Romans drained the marshy valleys between them to create markets known as fora in Latin. The interactions over time bonded the separate communities into a unified whole as the city came into being when these settlements acted as a group.
The Septimontium was a proto-urban festival celebrating residents of seven communities linked to specific peaks including Oppius, Palatium, Velia, Fagutal, Cermalus, Caelius, and Cispius. Three spurs of the Esquiline Hill formed part of this grouping along with peaks of the Palatine Hill itself.