Your fourth source includes one of the scientists who Damore cited. David P Schmitt's take is that "using someone’s biological sex to essentialize an entire group of people’s personality would be like operating with an axe. Not precise enough to do much good, probably will cause a lot of harm."
Hardly "many agree with him". And it bears repeating over and over that cherry-picking science facts (or even the opinion of scientists who agree with you) is not science. It's the same exercise those who believe in chem trails engage in. Let's stop. If you want information about the population Google hires from, do research on that population not the general public. You would be studying the smartest of folks, who are likely to graduate from the elite universities of the world. Studies of biological differences in the general population might have little bearing on the specific population Google hires from.