Nice try (-: Indeed it makes sense in English. In Hebrew it almost makes sense, but not all the way. First, in pastries (and cakes, salads, etc.) we'd say תפוחים and not תפוח. Secondly, if you order two things and use just the filling/flavor to specify which ones, presumably they're the same kind. Then in Hebrew we'd tend to use the gender of the implicit thing specified, rather than the gender of the specifier: if the thing is בורקס or just מאפה (both masculine) we'd say (oddly sounding, out of context) תפוחים אחד וגבינה אחד. If it's עוגה (feminine), תפוחים אחת וגבינה אחת.
I don't think the Hebrew sentence here would fit any context.
Actually you can talk about "one cheese" in English, and there are contexts where it is natural to do so (though I think it's less common in American English and more common in British English). Cheese can behave as either an uncountable mass noun ("There sure is a lot of cheese on this pizza") or a countable noun ("How many different cheeses are on the cheese platter?" To which the answer could be, "There is just one cheese left, the rest got eaten.")
I have the same question. This really needs to have a natural rather than literal answer - since a literal answer is not literal. There is no such thing as 'a cheese'. It is either a piece of cheese or a block of cheese or a cheese wheel. Or even, as you suggest, a type of cheese, though that seems unlikely in this context.
a/an is not exactly a synonym of 'one' as it is in many languages (e.g. French un/une). a/an does imply a singular item, but technically, it is the indefinite article. I would suggest, as airelibre said, that putting אחד in the Hebrew sentence emphasizes the number in much the same way that saying 'one' instead of 'an' does in English.
No, they say ugvina, not o gvina. This is technically the correct pronunciation due to some advanced rules only newsreaders and poets pay attention to, but don't worry about that. Whenever you hear u, just know it is "and", and whenever you want to say "and", just say "ve" as usual, because in casual speech nearly all Israelis do so.