Note that checking the statistical properties of the residuals is a crucial step diagnostic model checking. Our objective is to fit the a model that "squeezes that data dry", i.e. we get residuals that are white noise

 Now with regards to your questions

 1. The ACF of the residuals does **NOT** necessarily imply seasonality has not been removed. It might well be that the residuals follow an AR(2) process. Note that the ACF of an AR(2) is of the form

$$ \rho(\tau) = \frac{(1-\lambda_2^2)\lambda_1^{|\tau|+1}- (1-\lambda_1^2)\lambda_2^{|\tau|+1}}{(\lambda_1-\lambda_2)(1+\lambda_1\lambda_2)}  $$

where $\lambda_1, \lambda_2$ are solutions of $z^2+a_1z+a_2=0$

hence when $\lambda_1=\sqrt{a_2}e^{i\phi},\lambda_2=\sqrt{a_2}e^{-i\phi} $ 

(i.e. $0 \leq a_1^2 < 4a_2$), $\phi = cos^{-1}(-a_1/2 \sqrt{a_2}) \in [0,\pi)$

$$ \rho(\tau) = \frac{a_2^{\tau/2}\sin(\tau \phi + \psi)}{\sin \psi}, \tau \geq 0$$
where $\tan(\psi) = \frac{1+a_2}{1-a_2}\tan \phi$. 

As you may see, in this case ACF has the same form as the one of the screenshot. 

 2. Lower variance for the residuals means that MSE has been significantly reduced by fitting seasonal components. Hence it is plausible that the most likely explanation for the ACF is the AR(2) structure of the residuals rather than the inadequate explanatory power of the seasonal component.