As far as we know pregnancy will be available for most characters, at least the major ones. But this will be implemented progressively along the updates, starting with this one with Diane. The next update, Jenny update, will implement it for her, and so on. There could be exceptions.
As for how it works, we know two things. First, that there is a chance for pregnancy that varies from character to character, for example Roz will have a very very slim chance, while someone like Judith could have a very generous chance. Obviously that is if you cum inside, so in that sense the pregnancy is totally optional. The second thing we know is that there will be a minigame to successfully impregnate someone. I suspect that the minigame difficulty will be tied to the "probability" of impregnation of the character, but I don't really know. Maybe the chance is unrelated to the minigame.
As for how it will affect the game or the story, if I recall correctly the pregnancy will have 3 stages of 1 week each one. The first week without physical change, the second with a cute little belly, and the third with full grown belly. The dialogs will change and you will not be able to have sex with that character until she gives birth. Once born, the child will go to day care, and that's it. The children will not be characters and will not have any kind of content whatsoever. The mother will go back to normal, most probably as if nothing happened. You can have as many children as you want.