For 4(a), it may help to first prove the following.
Let $X_1, X_2$ be distributions over $S$ and $Y_1, Y_2$ be
distributions over $T$.  Then
$|X_1 \times Y_1 - X_2 \times Y_2|_1
\leq |X_1 - X_2|_1 + |Y_1 - Y_2|_1.$