Option $(B)$
$\bar{L} = \{a^nb^m|n \neq m ;n,m \geq 0\}$ This is CFL
$L^{*} = (a^nb^n)^*$ will always be CFL as CFL are closed under kleene-closure but it is not regular as it requires $b$ to match with the $a$ before starting with another runs of $a$.