Firstly, you cannot legally camp in Tatras. There are no designated places for camping and you risk being fined (66EUR in 2009 (1)). I am writing in EUR as it is probably easier to understand than PLN. The shelters will take EUR as well as PLN (on both sides of the border, I imagine).
There are many shelters on both Polish and Slovakian sides (map, in Polish) and the distances between them are not too long so you can easily go from one to another in one day. For the Polish shelters descriptions in English see here.
Sleeping: They usually offer a bed (with linen) in a dorm (capacity varies from 2 to about 15 people in one room) for 8-12EUR. Smaller rooms (2-4) are more expensive, about 15-20EUR. If they are full, most of the Polish shelters (PTTK - Polish Tourist and Sightseeing Society) are obliged to give you at least some space on the floor to spend the night on, but you will need your own sleeping mat and a sleeping bag for this if you don't like sleeping on hard floor. I would strongly recommend booking though, especially in the high season (July and August), as it will make your and the owners' lives easier. Just give them a call a day earlier, they all should have someone who speaks English.
Cooking: all these shelters serve hot food. The prices are relatively high, about 5-7EUR for a proper, traditional meal. Polish shelters in Tatras are famous for their apple pies ("szarlotka"). Usually there is a kitchen for the tourists, equipped with a kettle and a sink. Anything more than this (e.g. a stove) is possible, but not guaranteed. Hot water is always available from the kitchen staff.
PL and SK differences: I am not sure about the "floor rule" in Slovakia, but I imagine they can't turn you away if the weather is bad or it is too late for you to go somewhere else. The prices should be similar, but Slovakia uses Euro. The food will be as delicious as on the Polish side, only these will be Slovakian specialities.