2: More than one point in space makes a coordinate system, and more than one point is a prerequisite of relativity. (Source?) Plus, within the questionable physics models which allow for singularities, the notional difference between a coordinate system and a point is conspicuously broken in order to explain other things. But that's how we get vague terms like spacetime, descriptions for weird parts of the model.
3: I did prove it, and you can reproduce it yourself by going to the nearest mountain range and yodel. In other words, I don't need math proofs from within abstruse models to prove my point, so my argument is more sound scientifically. I proved "relativity" is nothing more than understanding the difference in change over space, which is a very obvious/observable thing, perhaps the most basic of all material existence, comporting to the idea that no two things can be one, or "occupy the same space".
Time measures change over space, a thing you witness firsthand when your yodel returns in echo from the mountain. If space did not change from point A to point B, there would be no distance, no coordinate system, and our yodel would not echo from anywhere. Without change over space there is no time, so that tells you which one is primary. The measurement of the echo, taken in time units, aka intervals, gives useful information. It does not however indicate anything of some model's out-of-bounds parameters, like what if the mountain had infinite gravity?
The measure of an echo could not prove a black hole, even by the very definition of a black hole, for an echo would not return (infinite inches of time til return). Ergo no measurement can prove a black hole. Only a model taken to mathematical infinity "proves" a black hole, and that is not real science, it's just math. Math proofs and scientific falsity are not the same side of a single coin. The observation yields math, not the other way around, or else I could say look here in my notebook, it's a real black hole!