You are right. It didn't cross my mind before.

if you mean non-normal in the sense that higher-order moments are not investigated, then that's just ordinary ARMA/ARCH/GARCH, and only weak stationarity is required. If you mean non-normal because a distribution different than Gaussian is assumed for the residuals, I'd say those are also quite exotic, but maybe that's just my impression

no, you could have $p_x>p_y$ and $r_x>r_y$. Example: x = {3,3,3}, y = {1,3,5}, then there are {2,2,2} and {4,4,4}.

you can't use stochastic dominance to create a full ranking, it's in my answer already. I see you suggested ELO for bridging that gap, it's quite an interesting approach, but in the end every total order is flawed in some way.

the breakdown point of the mean is not that low in a sample constrained between 0 and 5. Depending on the distribution and sample, the median could make bigger jumps than the mean for one or a few outliers.

"so you might prefer to use an ordering that allows more holistic consideration of ratings across categories" maybe suggest some. I don't agree that the arithmetic mean would be a worse measure than lexicographic dominance in any but very particular scenarios (app ratings not one of them).

cool. Maxima seems like a remarkable tool. is linsolve a Gauss solver for linear equations?

constant spectral density doesn't quite imply infinite variance. However, infinite variance is indeed possible with Cauchy white noise.

IID white noise passes the WW runs test. non-ID weakly stationary white noise could fail the test if the samples have different distributions while having same mean and variance.