Both the languages can be accepted by a DPDA:
$L_1 =$ start pushing element $X$ into the stack on input '$a$' ... start to pop $X$ on input '$b$' ... move to final state when stack empty and input = '$c$'
$L_2 =$ start pushing elements $XX$ into the stack on input '$a$' ... start to pop $X$ on input '$b$' ... move to final state when stack empty and input = 'epsilon'
So, (A) and (D) are False.
$L_1 \cup L_2$ is a CFL ... we can build it by having $L_1, L_2$ and an extra state ... and an 'epsilon' transition to both $L_1$ and $L_2$ from that extra state.
So, (C) is false.
$L_1 \cap L_2 =$ Phi because we have no string $a^ib^j$ where $i=j$ and $i=2j$ for $i,j \geq1$
and clearly $L_1$ is not a regular language
So, (B) is true.