Apart from an strong instinctual drive to love and care for children there's no "knowledge" about how to do that. Studies have shown that mother's brains light up differently in response to cries from her own child, and there's a strong anxiety when it's crying, pleasure when it's happy, etc. (Interestingly enough, I couldn't find any studies done on men, but I don't see any reason that fathers shouldn't react similarly)

But there's no "this is how you rock babies," "this is how you breastfeed," etc. I don't see how that would even work. Genes aren't magical. And I've seen some really clueless mothers...

I don't think so. I'm currently a stay-at-home dad of a 10 month old and we've found that my instincts regarding the baby are often better than my wife's. She often has no idea what to do and defers to my judgement.

Maybe, but even something you'd think is all instinct like breast feeding is a great deal of hit and miss. A lot of mothers find it hard to get the baby to feed, to the extent that most nativity units will have nurses helping mothers figure it out (whereas for some it just happens without the slightest problem), and it's not unusual for it to take days to learn to do it properly.

Humans are mammals, and have maternal instincts just like all the rest.

I'm not sure parental instincts include bathing techniques.

My instincts told me "no" when the midwife suggested adding olive oil to the bath water. I didn't listen. If you've ever fought a greased piglet you would understand what happened next.