The root of a word isn't the same as the meaning. Not to be funny, but I don't care if people don't care. There is a distinction between someone's biology and the role in society that is assumed to go along with it. Someone writing about gender studies definitely knows this.
Yes, but they're not just talking about roles in society when they speak of gender. They include cognitive, psychological and behavioural differences and conflate the two and claim both to be culturally constructed.