-I find this line of thinking very interesting. What makes people think that animals don't have their own laws that they live by?
There are laws that govern everything that exists. Down to the smallest particle, there are laws that dictate how things behave. If there was no law, we wouldn't be able to exist. Just as one example, what would any of us do without the law of gravity?
I have no idea what you are trying to say here. If we use the term "natural laws" as in gravity etc., then we are talking about scientific models used to describe the world. It's not the law of gravity that exist in itself, rather this is how we call the model we use to describe what we see in nature. Same goes for the concept of "survival of the fittest"; that term came to be to describe a simple observation: that when you look at evolution of organisms over time, it's the best fit that survive. This doesn't always mean the strongest. Nature isn't some free-for-all battlefield not because of some animal moral laws, but because behaviours like altruism can indeed be more beneficial for the survival of both the individual and the group.