Are these valid counterexamples to proofs for CF languages with Non-CF complements?
For the first question, $aaabaa$ is generated by the grammar:
$$\begin{align*}
    S&amp;\to AB \\
     &amp;\to aB &amp;&amp;\text{using }A\to a\\
     &amp;\to aaBa &amp;&amp;\text{using }B\to aBa\\
     &amp;\to aaaBaa &amp;&amp;\text{using }B\to aBa\\
     &amp;\to aaabaa &amp;&amp;\text{using }B\to b\,.
\end{align*}$$
Your attempt to prove the converse is incorrect because you assume that, when the string is split as&nbsp;$AB$, the part generated by $A$ must have the same length as the part generated by&nbsp;$B$. As the derivation above shows, this is not true.

For the second, you're correct that the class of deterministic CFLs is not closed under union. However, the class of CFLs is closed under union. That is, the union of two DCFLs is not necessarily a DCFL but it is definitely a CFL. The argument "$\overline{A}$ and $\overline{B}$ are deterministic context-free, so they are context-free, so $\overline{A}\cup\overline{B}$ is context-free" is implicit in the proof you quote.