The separation of powers is a concept created by Montesquieu that determines that the system of government of a nation must be governed by three different powers (executive, legislative and judiciary powers) that represent branches separate from the governmental system, in addition to monitoring each other, preventing the abuse of power and the concentration of power in just one branch of government.
In summary, the separation of powers allows separate branches of government to prevent actions by other branches of government. In representative democracy, checks and balances help to restrict powers between different branches.
Gender identity is defined as one's own personal experience with their gender. A person's gender identity does not have to correlate with their assigned sex at birth. Caitlin Jenner's quote above agrees with the fact that gender identity does not have to correlate with one's sex organs.