One: I believe that the difference between "claiming" and "owning" a right are significantly different things. Owning a right is a right that belongs to you and is yours to do as you please with. As to where "claiming" a right, is to take a right that was not previously yours. which is not true and is very important in realizing the difference. because you do not claim your natural rights, but own them.
Two: The colonists beliefs about rights were influenced by the writings of John Locke and other natural rights because they believed that the individual should have natural, unalienable rights that the government could not infringe on. So by adding the natural rights life, liberty, and pursuit of happiness were John Locke's influence on the constitution.
Three: A social contract is the people giving consent to the government to protect their rights in exchange for some of their rights. This is in relation to the concept of rights because in order for a social contract to work, a person gives up some of their rights in order to have the government protect thier natural rights and keep anyone else from infringing on them.