$L_2$ is regular, so complement of $L2, ( \sim L2)$, is also regular .
Regular languages are closed under complement. So, D is True.
$L_1 \cap L_2$ is context free.
Intersection of Context free language with Regular language is Context free. So, B is True.
$L_1 - L_2 = L_1 \cap (\sim L_2)$ is context free
Intersection of Context free language with Regular language is Context free. So, A is False .
$\sim L_1$ is not context free
Context free languages are not closed under complement. So C is False (May/not be).