Pumping Lemma Question: About the cases for y in the xy^iz criterion
Your proof doesn't work, since the pumping lemma only applies to large enough words. The pumping lemma states that if a language $L$ is regular, then there exists a constant $m$ such that all words in $L$ of length at least $m$ have a certain decomposition $xyz$ such that $|xy| \leq m$, $y \neq \epsilon$, and $xy^iz \in L$ for all $i \geq 0$. However, there is no guarantee for words of length smaller than $m$.

In your case, the word that you chose has size 8, which might conceivably be smaller than $m$, and so is not guaranteed to have the decomposition $xyz$ satisfying the properties stated above.

As an aside, if $L$ is finite than $m$ has to be larger than the size of all words in $L$ (why?), and in that case the pumping lemma cannot be applied to pump any word.