There may have been a Quirinius who became infused with the Romulus legends, but I find the idea that Romulus himself was a real person very unlikely. Both the stories of Romulus and the Sabines appear to be old traditions that probably reflect some legend - perhaps the latter symbolizes a war. But its doubtful that any of it really happened.
They did just find 10th century BCE woman buried in Rome, so certainly it was in place long before 753 BCE. Moreover, 753 wasn't even that common until Varro. Ennius and others places Romulus much later. We don't, can't, in fact, know what really happened, but it certainly wasn't as Livy told it.
Probably not. I think it would be attributing too much to Egypt. Perhaps indirectly, but its safer to just say no.
Not that I'm aware of. Cumae or Capua would be the closest (major) Greek colonies to Rome on the peninsula. The Latins and other tribes blocked off the Greeks to the north.