Regarding your parrot column, you state that if female parrots were shown to be as talented as male parrots at mimicry, that would disprove the hypothesis that mimicry was evolved as a sex attractant. I don’t believe that this conclusion would follow (i.e., your statement is possibly doodoo); there are certainly many instances of features or behaviors that benefit only one sex but appear in both, due to restrictions in genetics and developmental biology. One example: Why do men have nipples?
It may well be that female parrots can mimic sounds because there was no easily accessible evolutionary pathway that would give that ability exclusively to males. If you want to test the hypothesis, you need to remove the speech organs from some males and note the effect on their differential reproductive success.