That's not what I'm referring to, however. I'm referring to a difference between English and Portuguese, not a transatlantic different. You can say "civil society" and "a civil society" on both sides of the Atlantic; however, the terms are not interchangeable: the former is definite, whereas the latter is indefinite. English rarely marks abstractions with a definite article, but Romance languages commonly do. "Da sociedade civil" in Portuguese corresponds to the usage in English without the article, so translating "da sociedade civil" as "of a civil society" would be incorrect.
You are forgetting that Portuguese uses articles differently from English. "What is the role of a civil society?" is a question about civil societies in general, not a particular civil society. Does "Qual é o papel da sociedade civil?" only refer to a specific society, or can it per Portuguese usage refer to civil societies in general? That's the question you should be asking, not just translating things literally.
My answer "what's the role within civil society" sound right however: Qual é o papel dentro na sociedade civil. Appears not to translate how I expected. I though Dentro was within but it seems to closer translate to inside. Unless of course I have missed something completely here :-]