Finding Context Free Grammar for a language
Assume $m\ge k$. Then $$1^n0^m1^k0^p= 1^n0^{m-k} 0^k1^k0^{n+k-m} = 1^{n+k-m}\underbrace{1^{m-k}0^{m-k}}_{V \text{ if } m-k\ge 1} \underbrace{(0^k1^k)}_{U}0^{n+k-m}\,.$$
Such words are generated by $$\begin{align}U&\to 0U1|01\\ V&\to 1V0|10\\ T&\to 1VU0|1T0|11U00\end{align}\,.$$
Find a context free grammar for the case $m\lt k$ and you should be good to go.