Spectrophotometric assay by pNPP
For the first subquestion:

Using unit analysis, the answer is very quickly found: The unit of the slope $m$, assuming dimensionless values for the absorbance, is 
$$[m] = \frac{[\Delta y]}{[\Delta x]} = \frac{[\Delta A]}{[\Delta t]} = \frac{1}{\text{min}}$$

Now you need a volume in the denominator as well, so dividing by a volume seems like a good idea. Since you need the change in absorption per $\pu{mL}$ of $\ce{1X}$ solution, you divide the slope of the $\ce{1X}$ reaction by $\pu{0.24 mL}$ for the correct value.



For the subquestion with which you seem to have the most trouble: simply apply $c=n/V$.

You will find the amount of substance changed via
$$ \Delta n = \Delta c\times V = \Delta c \times \pu{1.2 mL}$$