Is the following language regular; context-free but not regular; or not context-free?
Denote your language by $L$. Notice that
$$ L \cap 1^*\#0^*1 = \{ 1^n \# 0^n 1 : n \geq 0 \}, $$
which should suffice for showing that $L$ isn't regular.
On the other hand,
$$
L = \{ 0^a1^n \# 0^n 10^b : n,a,b \geq 0 \} \cup
\{ 0^ax01^n \# 0^n1x^R0^b : n,a,b \geq 0, x \in \{0,1\}^* \},
$$
which should suffice for showing that $L$ is context-free.