Does the initial rate in the reaction of magnesium powder with nitric acid depend on the volume or the concentration of the acid?
The magnesium is present in form of a solid powder. Therefore, the reaction of magnesium with acid can only occur at the solid–liquid interface between magnesium and the aqueous nitric acid solution. Accordingly, the initial reaction rate depends on the surface area of the solid–liquid interface. For the experiments described in the question, the same mass of magnesium powder is used; therefore, the available surface area of the magnesium powder is approximately the same, too. Hence, as long as the added volume $V$ of the nitric acid solution is sufficient to cover the entire available surface of the magnesium powder, the initial reaction rate does not depend on the added volume of the solution. (Assuming a reasonable geometry of the reaction vessel, a volume of $V=100\ \mathrm{ml}$ should be more than enough to cover a mass of $m=5.0\ \mathrm g$ of magnesium powder.)

Furthermore, the reaction rate depends on the concentration $c$ of the acid at the solid–liquid interface. Therefore, the initial reaction rate depends on the concentration of the added nitric acid solution.

And finally, the reaction rate also depends on temperature $T$. Therefore, the initial reaction rate depends on the temperature of the reactants, i.e. the magnesium powder and the added nitric acid solution.

Hence, in order to obtain the same initial reaction rate, the concentration of the nitric acid solution $(c=1.0\ \mathrm{mol\ l^{-1}})$ and the temperature $(T=25\ \mathrm{^\circ C})$ should be the same during both experiments.