Localization of sound is primarily based on the time difference between the ears. Localization is also pretty precise, to within a few degrees under good conditions.
This wouldn't work well because in the frequency domain representation, different "pixels" have very different importance for the overall appearance of the image: The pixels at the center of the frequency domain representation represent low frequencies, so compressing them will drastically alter the appearance of the image. On the other hand, the corners/edges of the frequency domain representation represent high frequencies, i.e. image details that can be removed without causing the image to change much. That's the crucial benefit of the Fourier transform for compression: it decomposes the image into important bits (low frequencies) and relatively less portant bits (high frequencies). Applying compression that doesn't take that structure into account won't work well.
I think this persistent state is one of the main advantages of the notebook environment, or the Matlab workspace, which I guess it was inspired by. It allows you to quickly try alternative values for certain variables without having to re-calculate everything. Saving snapshots would not be feasible if the project contains large amounts of data. If you want to reset everything, just "run all" from the beginning, or use a conventional IDE with a debugger.
Minor point: What you describe isn't usually called working memory. Working memory is what you can "keep in mind" at any one point. It lasts for a few seconds and then has to be refreshed, e.g. by repeatedly saying a phone number to yourself in your head. Working memory is more or less synonymous with short-term memory.
What you describe is long-term memory (everything beyond a few seconds is considered long-term).
Edit: Too slow. Some more justification: Very broadly, one hypothesis is that working/short term memory is stored in the currently present activity patterns of neurons, which fade/decorelate after a few secodns. Anything longer is thought to be stored in the weights of the synapses between neurons (there are alternative theories but I like this one).
Sending before deducting the money seems like an obvious design flaw that should have raised red flags. Is there any explanation for why it was implemented this way, and why it wasn't spotted by the developers?