= Solution
Take $A=\{N\leftrightarrow S\}$ and let $s=1-p\downarrow0$ with
$$
q=s^{-3/2}.
$$
Then $sq\to\infty$, $s^2q\to0$, and $s^4q^3=s^{-1/2}\to\infty$. Part d gives $\mathbb P_{\mathrm{FK}}^{p,q}(A)\to0$.
On a four-cycle, $A\mathbin\square A$ occurs exactly when all four edges are open, because the two length-two paths from $N$ to $S$ are the only disjoint witnesses. Hence
$$
\mathbb P_{\mathrm{FK}}^{p,q}(A\mathbin\square A\mid A)
=\frac{p^4q}
{p^4q+4p^3sq+2p^2s^2q^2}
\longrightarrow1.
$$
Choosing $s$ sufficiently small gives the two numerical inequalities in the question.
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