Neither is the universe: we have (as far as we know) a limited number of matter and energy that can be converted to computation, which limits the size of an implementable system.
Real Turing completeness is necessarily theoretical.
We don’t know that at all. It’s a sensible assumption that the universe is infinite in size, and we have no indication to the contrary. The biggest impediments are the accelerating expansion of the universe (which however isn’t fully explained and thus may not be inevitable) and the heat death, which limits time for meaningful causal interaction.
