Curious6 said:
Is the exact nature of space and time known to us yet?
clearly it is not known
one way to interpret the question is to say "Do we know how to do geometry at all scales?"
People are not certain how to do geometry, I think, at very large scales because they do not confidently understand the shape of the universe.
No simple answer about what space was like a very long time ago---and so on---or how it curves if you go very far out in distance.
People are also not sure how to do geometry at very small scales.
It is difficult to see how to probe these very small scales, so as to discover if space is like what we experience at ordinary scale, or something different.
Perhaps also you could say people lack understanding of nature of space and time because they do not understand why it is bent by concentrations of mass and energy. Why should gravity bend space? One has the equation that says how it is bent, but no proposed mechanism to explain it.
to me the first obstacle seems to me that we lack understanding of spacetime at very small scales---the rest I would not want to worry about until the boundary of ignorance at microscopic scales is pushed back some more. but that is just a personal view
getting rid of the singularities of the Big Bang and Black Hole is one step in the direction of dealing with small scale, hopefully