However, using "kahviko", especially, indicates "one coffee", hence the article in the translation. Using "kahviako" (kahviAko - partitive) would refer to an unspecified amount of coffee ("kahvi" and "coffee" as mass nouns) and then having an article would be a clear mistake.
Senja, thinking about the English, the context would make it a known amount- you know, they're saying "...- here you are" so it's something that is obviously there in front of them, even if it is just given without being asked for. In a restaurant or in a house, it would be just as normal, or maybe even more normal to say "here you are- coffee", meaning the cup of coffee you asked for, or maybe just a nice surprise.
I agree, it is more common to ask: "kahvia?" With intonation going up in question, but I think "kahviko?" is more clearly a question and therefore better for a foreigner to learn. Also you need the "-ko/-kö" suffix so much in other sentences, so it is good to start memorizing it right away.
From the lesson tips (Finns do not plead like English speakers do) it is translated into English as please only because that is what one usually says in English.
Agree, come to think of it again, I can't work out when you would say one or the other