Science and reason alone are not a good basis for "rights".
"all men are endowed by their creator with inalienable rights", a powerful phrase but without some belief in a creator of higher level of reality what "rights" do you have?
Those that your government or society chooses to give your and protect for you?
Those that you have sufficient power to take and defend yourself?
If one does not believe in a higher power, a higher purpose or a higher level of reality, not only are your "rights" in trouble but so are your "ethics". Nietzsche had it right the madman cries out "god is dead" and the world descends into moral relativism and nihilism.
To lump moral relativism with nihilism is a bold move, to begin. The latter is rather inherently (and rightfully so) considered a negative thing. There is no reason to believe that moral relativism is a problem. I think the difference between moral absolutism and moral relativism is believing in some sort of natural moral code versus believing in a system of moral justifications. I think moral relativism is far more in tune with our intuitions than moral absolutism. There are few that would disagree that if there were a case when a man had to steal food so that his family would not starve, the man would have a moral justification for doing so.
And God certainly is required to guarantee any natural code of morality or rights anyway. We could just as easily say that people have certain rights just on the basis of their being human.
As far as the OP goes, I actually just wrote a paper comparing the philosophies of Hart, Dworkin, and Shue. But before getting into that, I'd like to take issue with your definition of a 'right'. The definition most commonly accepted by political and legal philosophers is that if one has a right, they have freedom from infringement (in terms of restraint or coercion again) on whatever action it is they have a right to, and all others have a duty to that person to not infringe on that right.
Continuing right along: I tend to align with Hart, who postulated that our rights are defined by our relationships; that is to say, our relationship with the government, our community, and our family. If I were the only person on earth, I would have any and all of the rights that I wanted. Our rights are limited by our relationships, we give up certain rights in a society because we benefit from other people giving them up to.
I also sympathize with Shue, who wrote most famously about human rights. I tend to agree that if it is the case that people have a right to have access to food and drinkable water, then others have a duty to not only refrain from infringing upon their access, but also stop those who are infringing as well as protecting them from future infringements if it is the case that they cannot protect themselves. Where I disagree with Shue is that there is even a right in this sense. Instead, I believe if one says that this right exists, then THEY acquire those duties.
I'll be back to give my opinion on the rest of your questions later.