Ozme
To deal with the wolf question (which is entirley contrived, by the way): no it's not hypocritical to kill the wolf, it's an act of self-defence on the part of man: man has the same natural rights as animals, and the right of self-defence is one of them. If another wolf perceived that this man was a threat to its existence, it would be justified in attacking him and killing him ... and so on ad infinitum. However, in the real world, this would be a ridiculous scenario; a consequence of pursuing logic to the nth degree. If you are trying to make me say that the legal system is bound to condemn a human being to death being for killing an animal, you have a long wait. Natural rights as I use the term (your 2nd definition, remember) fall outside any legal system.
I agree that moral and legal rights are invented by men, but these are not the "rights" I called natural rights earlier. Those rights are, to use your words, ones that are in "the nature of animals"; they are instinctive - inate. These are the rights that all living creatures take to themselves and which no-one can take away, save, perhaps, by imprisoning them. Rights may not have been the best word to use, "freedoms" might have been better. "Abilities" might be even better. Check a thesaurus for other possibiliities.
Better minds than mine have used rights in the sense I have used it, so I don't intend to apologise.
I maintain, therefore, that animals have the natural rights of self-defence, to hunt (or graze), and to roam freely. (This is not a definitive list, but indicative only.) These rights are not given by anyone. Animals can be given legal rights if the law makers wish to do so, but animals will never know they have them, and cannot enforce them.
The legislature can also impose duties and obligations on humans which benefit animals, and gives them quasi-legal rights. People would be expected to know what those laws are (ignorantia legis non excusat), and to break them would be a criminal act. The appropriate law-enforcement agencies would then take action.
I believe my earlier posts stand.
TYWD