"Quisiera un café sin azúcar, por favor."
Translation:I would like a coffee without sugar, please.
Coffee is a noncount noun which numbers cannot be used with. Use more, another cup etc
I agree that it is more common for people to say "I'll have coffee" and sounds a bit more natural. But "I'll have a coffee" sounds fine too and I've heard it a lot.
On a different subject: I have noticed that the Spanish speakers (both male and female) put a pause--or breath--between a request and "por favor." When I studied Spanish many years ago, that did not happen. Which way is preferred now?
I don't think there's a preferred way or a less preferred way. I think it's pretty much like in English: varies from person to person