Translation:The kitchen is at the center of the house.
Immery is right. But to honest, I too would have doubts hearing that. It's not applicable for "centrum" specifically (which is identical in all singular cases), but this might be part of a reason why we still keep locative case around. It's not always easy to hear that „w”, and then locative case may give you a hint that it was there.
Yes, that would work. Well, it would work 'accidentally', so to speak.
Kuchnia jest w centrum (the kitchen is in the center) - "centrum" is Locative.
Kuchnia jest centrum (the kitchen is the center) - "centrum" is Instrumental.
So it's only a fortunate accident that "centrum" is one of the rare words that has all the singular forms identical. If it was almost any other noun, the form would change, so it's not like you only have to miss out "w". :)
Yes and no. Their plural does: studium (singular is the same in each case), but plural is studia which do this:
So: centrum - centra/centrów/centrom/....; minimum - minima; maksimum - maksima
Also Greek neuter -os like (Rodos, Jolkos, Knossos... ) usually don't decline, but if we consider them to be masculine like Menelaos they do. Theoretically dictionaries show that this neuter words can be declined but nearly no one does it.