Why is "il caffe" used.... but then not spoken as "the coffee"? Better yet, when did 'il caffe" become YOUR coffee. Aren't there actual words for Your... like vostro/a ??? tuo? So... why wasn't a YOUR-word used?
Since "il" /the coffee isn't used... could we have just said... Prendi caffe senza... or said it as..... prendi il tuo caffe ??
I think you could use "il tuo" or "il vostro" in place of the definite article and it would also be correct. In English we wouldn't say "do you take the coffee..." as it seems to mix definite/indefiniteness, and it's important to remember that Italian employs the definite article in places where English doesn't (and vice versa). The most natural English translation to me is "do you take coffee..." but "your coffee" could also work.
I wrote "Do you take coffee without sugar", which was accepted. I have to disagree with accepting the "your coffee" translation. It may be implied under certain contexts, however its not explicitly stated. Also remember that many times in translating italian to english, the definite article is discarded.
There is no contracted form of senza except for senz before the letter "a", and I think that when you refer to something in general, senza is not followed by an article, but if you refer to something specific it is. At least that's how it seems to me if I compare it with the French "sans"