For example, if the the Zombies in the barn weren't fed chickens, would they go cannibalistic on each other? Can they go forever without feeding?
Don't know this one but
Also, I thought Zombies fed off of human brains? Why would they eat chickens, horses, etc. Is this a different make and model of zombie in TWD?
No these aren't your brain eating zombies. They eat meat. We have seen several instances of the zombies eating animals already. Just happens that humans happen to be in great number and a lot easier to catch and take down for a zombie than a wild animal is.