For 2.30:

It is a good step to set variables for each number in the $3\times 3$ square.  Let's not sum all the equations, instead add the equations related to the middle row, the middle column, and the two diagonals.

For 2.32:

Many of the questions in this chapter are about parity.  There is one very common and important fact about parity: if $a$ and $b$ are two integers, then $a-b$ and $a+b$ have the same parity (both are even or both are odd).  To see it is true, notice that the difference between these two numbers is $2b$, an even number.

For this particular problem, every time we replace two numbers with their difference, the new number has the same parity as the sum of the two numbers.  Since we only care about the parity of the result (even or odd), then it is the same result if we add the two numbers at every step instead of subtract.