Does this game have the ability for the villagers to automatically have kids? or do you have to do it yourself? I think it'd be neat for the game to "save itself" if you forget to play and not let your whole village die off.

Sorta. If you train a male villager how to breed he will take care of breeding as long as he is living. Once he dies, you will have to train another and so on. So it is on autopilot (if you will) so long as you a trained breeder.

but beware if you train a male he will impregnant every female in the village lol sounds like my ex

I love it when males do it

Yeah I had everyone on breeding duties and now Ive got every female in the village pregnant. My guys are legends (thankful my husband isnt though LOL)