The information content of a file is approximated by it's compressed size. If you have a 1Gb file of all zeros or all ones it will compress down to almost nothing, but a 1Gb file of random numbers will hardly compress at all.

We don't know. I wonder if the universe uses compression on stuff like that? It's a funny idea, but if information actually is mass/energy, you could measure that mass/energy, and if it was different for the cleared drive... Then you could prove that the universe is self-compressing. That would be a bit mind blowing.

A lot of "Ifs" though.