Translation:The Hungarian girl lives in this house.
It sounds a bit more natural to me with the present simple since living somewhere is usually something habitual rather than something that would be described as "an action that is taking place right now".
But it doesn't really sound wrong with the present continuous, either. I guess it focusses a bit on the fact that right now, she is occupying/inhabiting this house, or perhaps that she is actively making it her home (rather than merely existing in the house).
I don't think there was ez or az before together with a suffix at the noun. So: carefully composed.
These will be a whole list of new / modified words and the ton of pronouns will be fun too. Omitting personal pronouns was great, but myself, mine, at me, by me, for me... will all have their special suffix infected, or totally unrecognizable form like ez here. they will come back with a vengeance. lol