The various Origin Perks are mainly for role playing purposes, though some make the game noticeably easier (Gamine) or harder (Bambi/Meek). Beyond easy/hard, there is significant variation in how much they influence the game. Whereas it will be difficult to avoid pregnancy as a Broodmother, Nerd and Gym Bunny are more like a gentle push towards concentrating on Intelligence or Fitness, but can otherwise be played however you wish.
I am unsure about which "them" you are referring to with regards to the Broodmother; As far as I know there is nothing special there that is blocked from the other Origins.
As for Wildcard, some of the time (25%, I believe) it will pick a random perk in response to a situation. You would have to ask Sam about the exact mechanics at work, but the visible effect is that sometimes Sammy will automatically accept/reject a suggestion based on the random pick, or in cases where there would usually be more than two options to pick from there is now one or more fewer. Or the other way around: Options only available to specific origins/perks become randomly available to the Wildcard.
Some Origin Perks may be
gained later (Bimbo/Exhibitionist), but none may be lost.
As far as I know, pregnancy gets an individual roll for each instance of sex, adjusted for a whole bunch of variables.
There are plenty of pills in the game, but assuming "the pill" refers to Plan B, that is 100% effective the first day, then drops by 25% (or 20?) each day after that.