Around the Aventine there is a fair sized collection of Palmyrene inscriptions, which seems to imply a fairly close knit community of them there. The Palmyrenes are tricky to extrapolate from, as they were unusual in that they assiduously maintained their own language in inscriptions. It is difficult to know whether this means they behaved differently than other ethnicities or simply marked their presence differently. So there was seemingly an "ethnic community" of Palmyrenes, and may or may not have been for other groups.

Your other question is a bit trickier. The city of Rome was divided into fourteen regiones, and marker inscriptions indicate that they had distinctive characters, with particular rites, festivals, etc. It has been argued that these regiones activities correspond to different parts of Italy, but I am not certain how much real evidence is behind that.

There's a good overview of this topic in the first episode of Mary Beard's documentary Meet The Romans that discusses not only the demographics of particular neighborhoods, but the mechanism by which an immigrant's original culture would fade away in favor of Roman culture.

The series is focused mainly on interpreting the inscriptions left by average Roman citizens on tombstones, and it's Beard's conclusion that a given ethnicity did not contribute to where one lived. It's specifically noted that there weren't any neighborhoods analogous to, for instance, a Chinatown. Part of the reasoning behind this is that non-citizen Romans were mostly brought to the city as slaves, and rather than associating with a particular ethnic group, they associated with the particular family who owned them. Adopting Roman culture was a path to citizenship and status, and given the relatively high frequency at which slaves were freed it generally did not benefit them to cling onto their old ways.

That said, the region of Trastevere (across the Tiber) is singled out as an area in the city known for its immigrant population, having had a significant Jewish population since the Republican era. Jewish communities would have been one of the most notably different cultural groups in the city, largely retaining their own language, customs, and religion across generations.

Hopefully this is a decent starting off point, and I hope someone more versed in the subject than I can offer a more robust explanation.