This would be the simplest answer: בבית הקפה הזה מדוברת הונגרית. However, a better option would be: בבית הקפה הזה מדוברת השפה ההונגרית. Don't ask me why, but when we are talking about languages in hebrew, we like to assert the fact that it is a language right before we name it, for instance, השפה האנגלית, השפה הנורווגית, השפה התאילנדית, and so on.
No, I politely disagree with that. In my opinion, sam.eckman suggests to add השפה to make this sentence intelligible, but the problem is that the sentence בבית הקפה הזה מדוברת הונגרית just sounds awkward, I wouldn't use passive to express that. I would say מדברים הונגרית. The blank subject is used in Hebrew more often than the passive.
It depends on the circumstances. Obviously, the "language assertion" thing is not a rule, but it's something that happens quite often, probably in writing more so than in speech. I mean, saying אני לומד ערבית and אני לומד את השפה הערבית are basically the same thing, but the second option is somehow more appealing.. and less awkward.. if you get what i mean?? I know that's not a very good example but hopefully it can give you an idea of what I meant