C&D- Heat?

They definitely can. Both cats and dogs can go into heat, and if there's a cat or dog of opposite gender in the household and they haven't been spayed/neutered, puppies/kittens is a definite possibility.

During heat they emit hearts and think of hearty pet-couple thoughts and other heart-woohoo thoughts and generally act weird. That also seems to be the only time they mate on their own, without the owner sim encouraging them. I don't know if they have a higher chance to conceive during that or not, would make sense but not sure if they're coded that thoroughly.

That's just my observations on different pet genders living in one household, not sure how it works if the pet runs away for a bit and comes back pregnant, not sure how heat affects that since that's never happened to me.

I never timed it, it became quite normal thing in my household after a while so stopped paying attention (two female dogs, two male dogs in the household). Often, but not all the time.