Yup, that would be an impulse response, and if the room acts as a linear (and time-invariant) filter, then you can easily figure all that out, and the write-up is basically about testing if it's so and how good the reconstruction is.

And there is a way to toggle it: the icon which is orange can be tapped on and off, and you can adjust the "bass" which is built in with the ring around it. Also, it's likely to have no effect on voice, more complex arrangements will have an audible difference.

There is similarly an example on Wikipedia too, which got me interested: https://en.wikipedia.org/wiki/File:BinauralPaper.ogg.

Yes, it's called impulse response, used to capture convolutional reverbs, to model "real" sound stages like a large hall or what have you