In two-dimensional even parity, how do we determine the corner parity bit?
Do we look at the number of 1's in the corresponding column and/or in the corresponding row? 


Yes; you can do it in whichever direction is most convenient; it'll be the same either way.

In either direction, the parity of $z$ will be the parity of the entire data matrix (1 if there are an odd number of 1's, 0 if there are an even number).