Complexity analysis of recurrence with multiple variables
Since you know only $O$-bounds for the basic operations, you can not derive more precise bounds for $f$, nor $T$. Furthermore, if you had exact cost functions for the basic operations, solving divide-and-conquer recurrences exactly is very hard.

So, what the exercise authors probably want you to do is to say,


$f \in \Theta(m^2)$ (assuming that the bound for multiplication is tight, which they probably wanted to imply but didn't express properly) in either case, and
solve the schematic recurrence using the Master theorem (e.g. by substituting $f(m)$ with $m^2$).


You'll get out the correct $\Theta$ bound that way.