How do animals work?

Okay, so I have been reading the implemented guide about animal husbandry, and I am left with a few questions about animals:

1. What does familiarity do?
   I know about breeding and all. But what is the point of getting more familiarity? It seems like animals stop losing it at around 30 and are able to create offspring at 30, so why go above that?

2. Do I need to feed my animals?
   I of course know I need to feed them to gain familiarity and if they should reproduce.
   But do I need to feed them outside of that? Can my cows/Sheeps starve? Will they only give Wool/Milk if fed regulary?

3. How do I gain animal fat/what animal drops what?
   So, is there a graph that shows the different animal drops? Which animal drops animal fat/Hides, etc and with what chance? I could not really find a definitive answer in the guidebook or online.