What mods use resources of or are compatible with NoM?
There are a few that use the resources (which means they add compatible food) but not many come into my mind right now. http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=7817 is an example. If you use NoM, the food at the Inn can be used as NoM food. (otherwise they're just normal ingredients)
I think Annastia has NoM food in it.... and does Wizards Isles? I can't remember if it uses NoM resources or not.
Almost all mods are
compatible with NoM, unless they change the ID's of all the standard ingredients.
More specifically, are there any mods that add animals like chickens/cows/pigs etc that work with NoM?
That work with NoM? I am not sure. But the easiest way to find out would be to download the most http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=8707 of NoM and check the ReadMe (or the "compatibility" folder... or check the recent NoM Thread here)