Question about mapping reducibility
If $A$ is computable and $B$ is any nontrivial language (that is, $B \neq \emptyset,\Sigma^*$) then $A \leq_m B$. Indeed, pick $x \in B$ and $y \notin B$, and construct a computable reduction which decides whether its input is in $A$ or not, and outputs $x$ or $y$ accordingly.

Another issue you seem to be confused about is the meaning of context-free. The fact that a language is context-free doesn't preclude it from being regular. On the contrary, all regular languages are context-free.