Animals are not capable of sin, but they aren’t capable of making value judgments like a human is, either. But in possessing the ability to think rationally and make value judgments, and having free will would make any sentient being possessing those qualities capable of choosing whether to sin or not-at least that is my take on it...
They would also likely have knowledge of a higher power/supreme being/creator, as well.
I never watched Battlestar.
Yes, if you read Adam and Eve closely, the idea of knowing right from wrong is inseperable from the fall.