I don't think that the distribution needs to be linear... simply the correlation between N elements needs to be linear (or 1st order dominant). It works great for estimating multiple (e.g. different causes) small deviations (over multiple elements) from a global response. If you're looking at those larger eigen values, then you're looking at the dominant mode shapes of the eigen vectors of correlation.

As others have said, it's better for estimation (not for classification).

You keep using that word.

A multivariate Gaussian, for example.