In the sampling operation, all sinusoids are shifted down to the "natural baseband" by adding or subtracting some multiple of the sampling frequency that places the resulting frequency within +/- half of the sampling frequency. So for your example of 22kHz, that real frequency has two components: +22kHz that gets shifted down to -18kHz=22kHz-40kHz, and -22kHz that gets shifted up to +18kHz=-22kHz+40kHz.

Note that this "natural baseband" is an abstraction of our own invention. You can just as easily think of the spectrum as ranging from 0Hz to the sampling frequency f_s, rather than -f_s/2 to f_s/2. The fact that some prefer one over the other is precisely why fftshift exists.

Another way of looking at it is that sampling inherently does the mixing down to baseband. Although it may not be exactly the baseband you want if the spectrum isn't cleanly symmetric about a multiple of the sample frequency.

At a quantum-mechanical level, the wavefunction in the position domain is the Fourier transform of the wavefunction in the momentum domain, and vice versa - anything that constrains the position wavefunction to a narrow interval inherently also smears the momentum wavefunction...

Again, apologies if this seems pedantic. I know enough about quantum mechanics to be dangerous, but am no expert, so pedantic wording helps me keep things straight.

So why harmonic oscillators? The same analysis shows up any time you have a restoring force proportional to, and in the opposite direction of, the displacement. This shows up in springy things (recall the old mechanical engineer's adage: everything's a spring until it breaks), and fields of all sorts (electric, gravitational, magnetic, pressure).

1. "That is, sound waves are not made out of sines as real-word phenomena."

Sinusoids are the solutions to the harmonic oscillator differential equation (\ddot{x} = -w^2 x). The harmonic oscillator is an excellent model, or a component of excellent models, for many natural phenomena, including vibrating strings and columns of air, pressure waves in fluids, the list goes on. The utility of sinusoids is not due simply to their convenient mathematical properties, it's because many natural signals are sparse in the frequency domain, precisely because sinusoids do describe real world phenomena.

2. "A piston on a crankshaft produces "pure" sinusoidal up-and-down motion when operating at constant angular velocity."

Uh, no. The motion of a piston is approximately sinusoidal as you decrease the radius of the crank, but in no case is it a "pure" sinusoid.