$1)$$n_{Zn(NO_3)_2}=0,15 mol\Rightarrow n_{OH^-}=4.0,15=0,6 mol$$\Rightarrow V(1+2.0,5)=0,6\Rightarrow V=0,3 lit$
$2)$
$\begin{cases}Al:x mol \\ Mg:y mol\\Al_2O_3:z mol \end{cases}\Rightarrow \begin{cases}27x+24y+102z=9,03 \\ 1,5x=\frac{3,36}{22,4}\\1,5x+y=\frac{7,84}{22,4} \end{cases}\Rightarrow \begin{cases}x=0,1 mol \\ y=0,2 mol\\z=0,015 mol \end{cases}$
$a)\Rightarrow \begin{cases}m_{Al}=2,7 gam \\ m_{Mg}=4,8 gam\\m_{Al_2O_3}=1,53 gam \end{cases}$
$b)n_{HCl}=3x+2y+6z=0,79 mol\Rightarrow V=395 ml$
$n_{NaOH}=x+2z=0,13 mol\Rightarrow V_1=65 ml$