1.
$SA\bot (ABCD)$
$\Rightarrow h=SA=2a$
$S_{\text{đáy}}=AB.AD=3a^2$
$\to V_{S.ABCD}=\dfrac{1}{3}S_{\text{đáy}}.h=2a^3$
2.
$SA\bot (ABCD)$
$\Rightarrow A$ là hình chiếu của $S$ trên $(ABCD)$
$\Rightarrow (SC, (ABCD))=\widehat{SCA}$
$AC=\sqrt{AD^2+CD^2}=\sqrt{a^2+9a^2}=a\sqrt{10}$
$\Rightarrow \tan(SC,(ABCD))=\dfrac{2a}{a\sqrt{10}}=\dfrac{2}{\sqrt{10}}$
$\to (SC, (ABCD))=\arctan\dfrac{2}{\sqrt{10}}\approx 32^o18'$