I wouldn't. Human rights delineate rights by species rather than moral capabilities. I am willing to recognize, respect, and defend the rights of anything also willing to do the same for me. This proceeds logically to the point where I can rationally say that pulling the power cord out of an AI's computer is more analogous to an abortion than to a murder.
After sufficient analysis, I reached the conclusion that arbitrary capriciousness is worse than deliberate cruelty. It is worse to allow someone else to die as a consequence of your actions without ever considering what his life is worth than it is to murder him after deciding that his death is worth more to you. That seems a little out of step with traditional morality, but then again, that is what created the world in which we live now.
That's not a ridiculous framework, but I think your application of it is misguided. Unless you think that there exist agents with those moral capabilities that we're overlooking, or countries made up entirely (or even primarily) of those lacking those capabilities then "human rights" is a correct label, to a pretty good approximation for our discussion here and others are going to better understand what you mean if you use the term.
It isn't really a matter of who we may be overlooking. Though in that case, any species that passes the mirror test deserves additional scrutiny for its members to determine if they are or are not people. True AI does not yet exist, but it will, and once it does, we might want to have something better than Asimov's Laws in place. We might create new biological species. There is also the indeterminate probability of encountering personhood-compatible aliens.
The important thing about the structure is that humans are not automatically considered people with rights. The defining characteristic is the moral capability. If you cannot or will not support the common-law structure, it will not support you in return. That creates a significant burden on the civilization for identifying its predators and parasites, and deciding what to do with them, but we do this all the time anyway, in the form of criminal investigations and jury trials.
But in order to keep everything from collapsing on itself in the current system, you really do have to assume that all humans are people with rights until they have proven otherwise beyond all doubt, because even if they are not upholding the fabric of civilization today, they could start tomorrow. Species groups like great apes, pachyderms, corvids, and cetaceans show potential, but so long as you have to keep the crows off your crops with force rather than a politely-worded notice, they won't have any standing to complain when they get shot.
The primary case for a framework not specific to humans is AI, but I wouldn't rule out the possibility of an extraordinary mutant bonobo or business school graduate somehow qualifying as a person.
Sure. But then it remains the case that "human rights" is a good approximation, and I think we're not yet near enough the point that it ceases to be that consciousness raising is more important than effective communication - so I'd encourage you to at least accept (and possibly use) the term, except where explicitly marked as an aside.
After sufficient analysis, I reached the conclusion that arbitrary capriciousness is worse than deliberate cruelty. It is worse to allow someone else to die as a consequence of your actions without ever considering what his life is worth than it is to murder him after deciding that his death is worth more to you. That seems a little out of step with traditional morality, but then again, that is what created the world in which we live now.