Short answers, pulled from the story.
The National Academy of Sciences received its charter from President Abraham Lincoln on the 3rd of March 1863. This legislation created a private organization dedicated to providing scientific advice to the federal government during times of crisis.
Florence R. Sabin became the first woman member of the National Academy of Sciences in 1924 after decades of male exclusivity. She broke barriers by gaining election following her extensive contributions to science.
Current records show there were 2,382 active members and 484 international members as of recent counts. Approximately 190 of these individuals have won Nobel Prizes for their groundbreaking work.
A maximum of 100 members may be elected annually while non-citizens face a cap of 25 international members per year. New members and international members have been elected annually since 1863 through a rigorous peer review system.
Richard Feynman resigned his NAS membership because he perceived the Academy's elitism and in-group favoritism. He outlines these reasons in his published correspondence titled Perfectly Reasonable Deviations from the Beaten Track.