So, "Süt a nap" literally means, "the day is baking"? But one translates it as, "The sun is shining"? Can it be said on a cold, clear day, when the sun is shining, but the temperature is 0 С?
Süt means both 'bake' and 'shine'. It's a similar concept of warmth coming in. And nap means both 'day' and 'sun'. Lots of homonyms here. :D
But I think "cook" is still a better translation of "süt" than "bake" is. Cooking includes both baking and frying. Baking does not include frying. (If I understand right, süt refers to the kind of cooking where things can get brown and crispy.)
You're wrong in that aspect that Hungarian makes sharp distinction between cooking and baking/frying/roasting.
Ah. So "főz" means specifically boiling-type cooking? (In English, cooking means "preparing food" in a broad sense, usually with heat involved somehow, including boiling/baking/etc.)
Indeed, "főz" is boiling or steaming, and "süt" is only baking, frying and grilling. It may help to consider the temperature—in boiling and steaming the applied temperature is above 100°C but close to that; for "süt" the temperature is usually higher than 150°C. There is another way to prepare certain types of food that involves water about 90–97°C hot, but in this method boiling is a serious mistake. This is called "abálás" (the verb is "abál"). If you're not afraid of fat and spicy things, you may want to give a try to "abált szalonna" that is prepared with this method and it is covered with red paprika and saturated with garlic. It must be great against vampires and fitness / health care experts ;) :D
Do you want a common Hungarian tongue twister? Here you are: "Mit sütsz, kis Szűcs?" ("What do you fry, little Furrier?" — where furrier appears as a family name). In a longer version one more question is added: "Sós húst sütsz, kis Szűcs?" ("Are you frying salted meat, littler Furrier?")