Absolutely, the Etruscans were heavily involved with trade with those cultures, so they were also influenced each other. However due to a lack of Etruscan literary sources and that we do not fully understand their language, much of what we know about them is from a Greek and Roman persepctives, so it is slightly skewed. The Romans are commonly viewed as being culturally dominant in Italy, rather then being part of a large network of interaction, with the Etruscans tending to be forgotton in the cultural landscape in comparison to the Greeks and Romans. By describing the Etruscans with terms such as 'Romanisation' sort of implies that the Romans influenced the Etruscans in a one way exchange, rather then a complex cultural exchange. Part of what made the Romans so successful in their conquest of Italy was their integration of cultures, rather then complete replacement. Artefacts like the bronzes in this article demonstrate this integration of cultures, even within Roman control.

> I thought that it was history that Rome was just a small city in the periphery of the Etruscan city-state coalition

While it is a common cliche to say Rome was "just a small village" it is worth noting that is mostly Roman self mythologizing being accepted uncritically--By the late sixth/early fifth century Rome was already the great power in central Italy. As an illustrative proxy, the temple of Jupiter Optimus Maximus one of the largest in the entire Mediterranean, larger than any Etruscan temple.