Not quite, compression enables you to simulate / represent / encode x data with less than x memory.

Only for those inputs that are compressible.

If a compressor can compress every input of length N bits into fewer than N bits, then at least 2 of the 2^N possible inputs have the same output. Thus there cannot exist a universal compressor.

Modify as desired for fractional bits. The essential argument is the same.

Would the compressibility of the state of the universe be useful to prove whether we are in a simulation already? (i.e. it is hard to compress data that is already compressed)