Religion is antithetical to survival of the fittest, in that the message of religion is that the strong should not kill the weak, while a purely Darwinian ethic would suggest the opposite. Thus morality is the direct offshoot of the idea that a god or gods could punish you for behaving in a selfish, animalistic way. You need not be religious to behave morally, but the intellectual foundation for your moral behavior will be non-existent.
Religion is not the main reason people act ethically or morally. There are plenty of wicked people who do horrid and evil things in the name of their religion. And there are many non-believers who are kind, honest and fair. Ethics and morality, both good and bad, are usually passed from parent to child. It's not always possible to know the source.
Religions are a source of metaphysical and spiritual comfort for many, but the teachings for living ethically and morally are often the same. It's really just social compacts restated in different ways. Even atheists and those that don't believe still follow such social compacts, so no, religions are not alone responsible for morality
While religion helps many people live morally and ethically, it is not the main reason that mankind at large chooses to live in that manner. Basically, when mankind agreed to come together to live as a civilized unit, it was agreed that doing so required members of society to make certain concessions. Those concessions evolved into what we now know as morals and ethics.