I don't know what you mean by "decided to use the R2" The domain is not a "choice"! The problem says "f(x, y, z)" so f depends upon the three variables x, y, and z. The domain of the function is a subset of . Of course to be able to take that square root we must have . What is that set?
The "level sets" of levels 0 and 2 are the graphs of and which are equivalent to and . What are those graphs?