Additionally, how large part of the population would actually benefit/use the different public facilities that we now think of as Roman such as public baths, theatres, colosseums etc. Would it be possible for only the urban population or did the rural population also have access to such facilities?
Any particular province in a particular period?
You see some areas had a settled history of urban settlement (the Near East, Ionia, Greece, Italy, North Africa - essentially the Mediterranean provinces) had long been urbanized in long established cities and the Romans simply were an incoming Administration. Naturally the Romans would "Romanize" towns and cities over time (to varying degrees), but that doesn't imply there wasn't urban life there before.
They did certainly build whole new cities on a Roman model in Northern Europe, London being first to cross my mind as an example, Trier being second.
As to the use of facilities. I'm not aware of any impediments to a peasant just moving into the urban center so I don't see why they couldn't in theory access the public facilities too. However, it's possible there was Roman migration control laws in place that I am not aware of. If anyone has sources or examples of these (if they do exist) I could read about I'd much appreciate a book citation or link to the source.