1. Who gave them these rights? God did of course. Just being alive does not constitute power or freedom. A tree is alive but shares no power in this world, nor a fish, or bird. They can not speak. They can not reason. Therefore they can not know the difference. A fish will keep swimming. A tree will keep growing, and a bird will keep singing. Now mammals will show that they know the difference, yet they only have two responses, flight or fight. Love by a dog is actually the fight response. It stays and reacts to what is given to them. Humans are different. They can actually initiate the situation. They can respond, or not. They can reason, or not. They can speak. They have authority. Given by God. Yet to each fellow human they have responsibility, something else animals do not have. This responsibility means that some need protection from the powerful, hence rights.
2. What constitutes a human? At what point does man gain rights? Was it Neanderthal man? Was it Homo Erectus? Was it Australopithecus afarensis? Was it a primate of the first kind? Or was is algae? Is it fair to say since we all come from the same single cell organism that Homo sapiens are the only ones with natural rights? Yes. Because they are the only man created by God. The others are just figments of man's imagination (flawed science)they are not man; or they are just deformed humans (those who do not meet high standard visual desires of others).
Using science (deism and enlightenment) to show once again evolution is not a valid theory.