Grr! What kind of thought lead you to such conclusion? All things you have named is actually have the same meaning in the classical case. I have provided example of the brick wich is splinted into two pieces durring free fall, it is an event, in classic and in the SR kinematics. The relativity exist in classical mechanics too! The different inertial frames exists, so the relativity corresponding to this frames exist too... The classical mechanics relativity in the name of holy Newton, Hamilton and Lagrange can be self-sustained, it's no need this 'relative-relativity' things to describe models. And it's working a very well, and this is actually the case where we totaly no need non-classical things.Well, you say "classical" in the title, but then in the text you use words like "absolute", "event", "invariant", "frames", and "observer" throughout all of your posts, and you never specify ##v<c_s<<c##. All of which essentially require answers to be in the context of relativity if they are to be physically correct answers. I don't know how it is possible to address a question in those terms without relativity.
As for myself, I am not even started to restudy my university course of classical mechanics which I have some studies long ago, but indeed it is a very fundamental and a very crucial point in learning of physics!