I shall address your question concerning reason and the law of nature and shall leave aside the last two sentences concerning morality.
It is true that Locke believes that reason allows those even in a state of nature to know the laws of nature and, therefore, to follow them. Thus, in principle, one might think that people could live in harmony in a state of nature, guided by reason alone.
Unfortunately, when people live together or interact with other, which we must necessarily do, disagreements will sometimes arise. What's more, when someone is a party to a dispute, they are not always able to reason properly concerning the dispute. This is a fact of human nature; we are not always good reasoners when our interests are involved.
In order to adjudicate such disputes, we need a third party to help us. Thus, because people will inevitably come into contract or property disputes, and because they cannot always adjudicate their own or their neighbors' and friends' disputes rationally, we must establish an independent judiciary, so to speak. In other words, we must agree to give up our natural rights in exchange for civil rights, which will make an independent system of justice possible.