Polish/Hungarian in Rome
I don't know of any, but I would go sniffing around the Polish church (via dei Polacchi? in any case on or near Botteghe Oscure) and perhaps ask. The soon-to-be-Blessed John Paul II had Polish nuns to cook for him.
Simply eons ago, before there were any foreign restaurants in Rome, there was a Hungarian place at the bottom of the steps leading up to the Markets of Trajan on Via IV Novembre. I never went -- could never persuade anyone to go with me -- and it eventually closed. I am unaware of any replacement, but if I really needed to know, I'd call the consulate.
There absolutely is a Polish restaurant in Rome. (I highly doubt it is the only one but it's the only one I know!) It's called Osteria Barbazza and is located at Largo Barbazza 32/33. (Sorry I can't add a link!) You can get there by taking the Metro A to Battistini then switching to the Bus #46. Take it 7 stops and get off at the Capecelatro stop. The restaurant is a few minutes walk from there.