So when a gene changes, that is proof of evolution. But when a gene does not change, even when it was expected to, that is also proof of evolution.
Genes that do not change over time imply that their function was critical enough to not allow the change without drastically impacting the survivability of the individual (and the species, as the change accumulates in the species' genome). It's not as if all genes are randomly changing to whatever they may change to. It all depends on the selective pressures and the allowances that permit the accommodation of those changes.
No. What supports evolution (not proves, since no scientific theory is ever proved) is that the patterns are consistent, in conformity to evolutionary patterns of relationship, across the great diversity of species.
So, for instance, as the article says, most sex genes evolve fairly rapidly, and so vary quite a bit among taxa. However, if you find a particular gene that doesn't vary that much between, say, deuterostomes and protostomes (these are the two main divisions of bilaterally symmetrical animals, with protostomes including arthropods, nematodes, molluscs, et al, and deuterostomes including Chordates, like us, sea urchins, et al) then -- if evolution is true -- it must also vary little, and in fact even less, when compared across diverse species within each of these groups, and likewise within each progressively smaller subgroup.
Any exception to such patterns must be correlated with specific and identifiable divergences in form or function.
In fact there are many, many, many thousands of very specific genetic traits and patterns -- variations among homologous genes, appearances of new genes, divergences of gene families, chromosomal mutations, transposable elements and relict viruses, etc, etc -- that must independently, but simultaneously, conform with evolutionary patterns of relationship. Collectively there have to be millions of opportunities for elements of this data to flatly contradict evolution, but so far that never happens.