You can't actually get pregnant until a certain event happens and iirc the doctor pretty much tells you that you are a magical baby factory. I'm not 100% on when you can start getting preggers.
You have a fertility rating where 0 = no chance, and 100 = guarantee.
Taking a birth control pill every morning sets it to 0 until you goto sleep, so it lasts even until the AM.
If you have a certain person in mind that you want to get preggers with, you can take birth control every morning, and with a combination of save scumming and fertility meds, basically choose who gets you preggers. (Fertility meds do stack so you can take 5x Fertility II's and reach 100%)
The game does actually keep track of who's baby it is and there are even dialog for cucking your current BF if you are in one.
When pregnant your fertility goes to zero until the parasite is born. The game doesn't really change anything until you progress to baby bump stage, which takes a few days. Once you get a baby bump, the game changes in various ways which I'm not totally familiar with. But for example, in one scene Santa Clause didn't want any baby bump Manila pussy, so instead the scene shifted over to Jason knocking up Santa's bitch.
You can skip the baby bump stage completely by taking a drug but I don't remember what it's called. Like Preggo-X or Preggo Max. (I don't have the game installed anymore)
When on Preggo-X, when you would normally start showing a bump, you instead just start your morning off with a required quest to goto the hospital and giving birth.
In this way, you can skip any interruptions to the story that would be caused by a baby bump.
Going by the game's story, the Kami's want to breed Manila so that they can survive, and you can actually get knocked up by Kami's during the game. (John Doe and Santa for certain, possibly others) But I don't know if that causes anything special to happen in the game. Seeing as how that is one of their main objectives, you'd figure having Kami kids would impact the story, but who knows~