Thats a big broad and vague as a question.
We dont know how big space is, we know how big the observable universe is if thats what you mean, we dont know how long space goes on after that, because the observable universe is all we can ever see.
We dont think its looping back around behind that because we have measured the curvature and it seems flat.
You have to elaborate what you mean with the second question you ask. Most things you mean “we know” is probably a theory based on multiple observations. Like for example we know the universe is expanding by observing that all galaxies move away from each other.
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