Are these two languages regular?
Hint for (1): consider a different type of value, $\mathrm{value}(s) = 1$ if $s$ ends with $z$, and $\mathrm{value}(s) = 0$ otherwise. Define the language $L$ as in your case, and consider $L \cap x^* z y^* z$.

Hint for (2): consider the language $L_\alpha = \{xy : \mathrm{value}(x) = \mathrm{value}(y) = \alpha \}$. What is the relation between $L_\alpha$ and $M_\alpha = \{ x : \mathrm{value}(x) = \alpha \}$? Is $M_\alpha$ regular?