Autocorrelation matrix derivation
You get a diagonal matrix because the values of $\eta(n)$ at different times (sample indices $n$) are uncorrelated, as shown in your first equation. This means that all off-diagonal elements of the auto-correlation matrix must be zero (they equal $E[\eta(n)\eta(n+m]$ for $m\neq 0$). Only the diagonal elements are non-zero, and they are equal to the variance.