You got a WASP mother pero me estás hablando de generes? What's your linguistic background? I think the English word would be "types," or maybe, if you want to get fancy, ""archetypes."
I've got mixed feelings about the Mary Sue thing--that is to say female characters that are automatically good at everythig. On the one hand, people say that it isn't sexist because there are "Marty Stu's", the male version of it. But the reality is that the Mary Sue was the start of the trope because it is so offensive to people that a WOMAN could just be good at EVERYTHING that people had to come up with a word for it. Looking back, it's trivial to find a plethora of Marty Stus that escaped public notice for years (James T Kirk, James Bond).
I think it's really a question if we're going to allow girls the same access to infantile power fantasies that we do boys, and that I guess I do not have a problem with, though as I grow older I'm increasingly uncomfortable with the wish fulfillment aspect of media.
That said, I think Sue/Stu does rob your character of potential avenues to demonstrate development and it makes the narrative less interesting, so you have to make up for it somehow; unless it's just a stupid show for stupid children, something Disney has decided it is making exclusively these days.
And I agree with 100%. Cameron's women are amazing examples of how to make women action heroes WITHOUT turning them into stereotypical men.