Oh boy, something in my field!

So Roman paganism is a bit of an odd term because the pantheon shifted a lot, and the same gods weren’t always consistent, but you do have definite stable characters. Now Romans weren’t super concerned that you specifically worship their gods, at least not during the imperial period, in fact there was a sizable cult of Isis in Rome, but they were concerned with obedience to the state. I focus my research specifically on North Africa so I there may be variations in different areas, but the general trend is that urban areas tended to be heavily latinized (Carthage in NA, Lugdunum in Gaul, etc), while rural areas tended to have a stronger presence of local faiths that would more slowly shift over to possessing more Latin elements. So in short, yes. Roman paganism was practiced outside of the Italian peninsula, but it’s form wasn’t always the same, and it also depended on if you’re talking about Roman colonists, or people who were simply absorbed into the empire, as well as the social class of who you’re looking at.

As to your question about the actual city of Rome and religious practices there, the answer is also yes. Rome by the imperial period was a very multicultural city with a plethora of different religious groups, so you did have plenty of people worshipping their native gods, but there were certain occasions where they were expected to sacrifice for the state. While the Roman state (usually) didn’t care much about your private worship, you were expected to make certain sacrifices, such as those made for the emperor’s health and longevity, as seen In the Passion of saints Perpetua and felicity where several Christians are sentenced to damnatio ad bestias because they refused to make a sacrifice on the birthday of the junior emperor Geta on the basis that it would be betraying their belief in the Christian god.