Gender is not a biological concept, period; that's sex. Your body is also distinctly not "one or the other", given that a large portion of the world is born with one of several intersex conditions.
No, a very very small portion. Gender doesn't vary independently from sex, you'd be hard pressed to find a stronger correlation. It's misleading to consider them as totally separate things.
Redefining gender is an uphill battle. I won't wish you good luck in doing that, I'd prefer coming up with a new term for this goal.
What sort of "intersex conditions" are large portions of the world born with? What do you mean by "large portion?" Like 50%? 30%?
Happy to follow a link if you don't want to type it out and would rather paste a URL