It would not upset the ToE one bit. All that would happen is that someone would declare *Look, a rabbit is a living fossil after all.*
Oh, it certainly would. Current evolutionary theory would not accomodate any of the things I listed. A precambrian rabbit would be very disastrous for our current theories about the evolution of rabbits, and mammals in general. We would have to come up with some other evolutionary mechanism for mammal development.
Detection of non-nucleic acid heredity would be disastrous on a more fundamental level. Evolution proposes that all life is genetically related. A life form that doesn’t even have nucleic acids as a hereditary mechanism could not possibly be genetically related to those that do. That would certainly falsify the idea of common descent.
Of course, most creationists suffer from the fallacy of false dichotomy. If any of these things were found and evolution falsified, that does not mean that creationism wins. There would be a new SCIENTIFIC theory formulated and tested against the available evidence. I’m sure creationists would dislike the new theory just as much as they do evolution. (BTW, you notice that most scientists spend their time gathering evidence for evolution, not trying to falsify creationism; they understand that false dichotomy is a fallacy.)