"...It's sort of like the police car driving past your house: the siren changes note. This effect (Doppler) is because the relative space of the air being affected is warped massively ... without the movement it might strike <this> air molecule, but with the movement, it strikes <this other> air molecule, in a different location. This gets "translated" by our ear to indicate a change in pitch, or an alteration in the note we "hear". This is merely just a weakness in our auditory system to lack the ability to account for the movement of the police car's siren...,
not so...The siren does not change note, it is the received signal that appears 'changed'. The change in pitch is due to the relative movement of the source and has nothing to do with any changes in bumping molecules except that's how the sound [wavelength or pitch] is transmitted. And that happens whether the source and receiver are stationary or in relative motion with each other. That is nothing like the transmission of light: Light requires no transmission medium as does sound.
"So it is with the light waves. "
As explained, no, it's very different than sound
"...With light waves received from distant objects: the very "space" or "nothingness" (or Higg's field/vaccuum of somethingness) (between us and the distant object) that is carrying the wave [carrying the energy pattern that we call "light"] i*itself* is growing..."
Space is NOT nothingness...it has vacuum [or zero point] energy for example. And includes spacetime of relativity.
"...It's like the universe is a police car driving rapidly past our house; but instead of one piece of it moving (the car), it's all moving: every part of it. Every part of the universe is growing outwards from each other part of itself..."
This is redshift [due to cosmological expansion] as contrasted with the doppler shift of peculiar [local] motion.
"Hence, exactly like the police car siren (which is trying to manipulate air molecules, which we call "sound"), the light from distant universes is also warped because of this movement."
no, it is quite different. And neither involves 'warping' nor 'manipulation'. Sound signals simply cause air molecules to vibrate and that's what the ear records..slight changes in pressure.
"Looking in the specific sense: the peak of the (light/audio) waveform impacts a slight different part of space than it would, without the expansion. Likewise the trough of the waveform impacts a slight different part of space that it would have, without the expansion. So with sound, as it is with light."
No, again, very different concepts between increasing distance in cosmology and air molecules carrying the energy of sound.
"Indeed; the concepts of red and blue are just humanity's interpretation of the different wavelengths of light (EM radiation), and it's using these arbitrary units/colours which perhaps causes confusion."
There is no confusion: The ear distinguishes different sound wavelengths and our instruments as well...as spectral shifts.
"...It is not correct that "red light" is being emitted by anything. What is being emitted is light (white, presumably, in this example), and as it travels to us, it is warped by the expansion of the universe: i.e. the expansion of the medium carrying the signal (relative to what we'd call "normal").
This is correct: the source emission characteristic, say a fixed wavelngth, is what it is. It is our measurement of the received signal that is changed by the relative cosmological expansion or motion of the source relative to us.