... we got a bit off track here because the OP clearly defined rights as including a moral component. We agree (as the OP does) that "communal rights" is a contradictory concept.
The last statement you made that I would like to explore is this:
"The ability to argue and the act of argumentation are no more proofs that rights are valid than the ability to steal and the theft itself are proofs that the thief is the rightful owner of the recently acquired property."
Again, the ability to do something says nothing about a moral component of whether or not that act is justifiable. We agree on that. And OP included a moral component in his definition of rights, indicating he agrees, too.
So, your point addresses the proof of whether or not rights exist at all, correct?
I previously said that rights are a concept and do not exist in the physical world. Agree?
Furthermore, the concept of rights is an abstract way of identifying what sort of concrete actions we SHOULD (or should not) take with regard to others. Agree?
Although people do not agree on what rights really are or should be, that lack of agreement is irrelevant to whether or not there MIGHT be some way to arrive at objective standards of what rights should be in a civil society. Agree?
All of this "should do this" or "should not do that" has to do with making moral decisions regarding our actions as it relates to other people. Agree?
Therefore, the concept of rights necessarily includes a moral component. Discussing an action that does not include a moral component is a discussion of something other than "rights." In other words, ability to take an action is a different topic of conversation from discussing the moral judgement regarding taking that action. Agree?