[1] I think sound stage is like you are standing in a circle where the “instruments” are spread across from the center hence a VIRTUAL RADIUS. While imaging is how much VIRTUAL ANGLE your line of sight center to the sound source the Sound Engineer intend you to hear.
[2] It is virtual because a speaker or headphones can only replicate the sound radius & angle. The degree of accuracy depend on how the sound engineer mix the monaural audio. I believe it is a pretty complicated thing. For a starter, a weak sound contrast means further hence greater radius from center. It must be contrasted to a louder sound. That’s how the sound engineer emulate depth or
radius.
[3] There are several techniques to create a sense of depth and stereophonic location, even using 2 speakers with a subwoofer in two dimensional space or simple stereo headphones can do the trick of us hearing things from above or below you.
[4]
Ultimately, A sound’s image engineered for speakers is not appropriate to listen on headphones. And vice versa.
[4a] The Beatles’ Sergeant Peppers engineered for stereo speakers. The imaging would be bad if played in headphones.
[4b] If a modern music/games is designed for headphones, you can still hear it on speakers but it would be in a weird imaging position.
[5] The only thing to remember is now people mix to use in a 5.1 or even 7.1 or Atmos environment. Mixing Dolby for headphones is different from Dolby for speakers.
[6] You can now even mix surround 5.1 on a regular stereo headphone. No need for a specialty room with real surround setup.
1. That's not really what you are supposed to hear. What you are supposed to hear can be better described as like you being in the audience in say a concert hall, with a stage in front of you. This stage has width, a left and right, and also depth, a front and a back, where a performer at the front of the stage will be closer to you and a performer at the back of the stage will be further away. However, this analogy isn't entirely accurate, for example unlike a real stage, the "stage" in a music/sound mix can have almost infinite depth, although typically, music mixes don't employ/use as much of that available depth as sound mixes. Your analogy appears to use "radius" as the depth (front/back) of the stage and "angle" as the width (left/right).
2. Technically, speakers or headphones cannot replicate either left/right or front/back, it's all effectively an illusion. The illusion of left/right positioning in the stereo image is achieved by varying the amount of sound energy routed to each of the speakers. For example, if the sound energy is routed entirely to the left speaker the sound will appear to be in front of you, at the left most extreme position of the "stage", while if the energy is routed equally to both speakers it will appear to be in the exact centre of the "stage" and if the energy is routed say 75% to the left speaker and 25% to the right, it will appear to be halfway between the centre and left most "stage" positions. This aspect of the stereo image is not a "complicated thing" in fact it couldn't be simpler, it's called "panning" and the sound engineer controls it with a "pan pot", a simple knob. This can be done with a high degree of precision because modern digital mixers typically divide this panning into about 200 steps (100% left to 100% right). Depth on the other hand is trickier because it is entirely dependant on the perception of distance, which has several factors, all of which are relative rather than absolute. A distant version of the same sound will be quieter, will have less high frequency content and will have a greater ratio of reverb (sound reflections) to direct sound. "Stage" depth therefore doesn't have a simple, single control but is controlled by a combination of different tools, fader for volume, EQ for frequency content and reverb for sound reflections. In addition, compression is a front/back control, more compression will add to the perception of the sound being nearer the front of the "stage" (closer to you).
3. This isn't really correct. Hearing things from above or below (the vertical plane) is extremely variable from person to person, depending on their individual pinnae. We can't create a perception of the vertical plane on a commercial mix designed for speakers and even with headphones, it's very hit and miss and therefore typically not attempted.
4. Generally that is at least somewhat true, although most music recordings/mixes, particularly more recent ones, are not exclusively engineered for speakers. Therefore, even though the imaging would be different on HPs, it might not be "inappropriate".
4a. If you're talking about the original mix, then probably. Stereo mixing in the 1960's was rather rudimentary compared to what was possible in the 1980's.
4b. Yes, IF it were designed exclusively for headphone playback.
5. As far as I'm aware, no one creates commercial mixes for Dolby Headphones.
6. Again, not really. In theory it's possible but in practice it doesn't work very well. A surround mix created on headphones will translate unpredictably to an actually surround sound system. This is why all the very expensive, multi-million dollar surround mixing facilities haven't ceased trading!
Without wishing to sound too harsh or discourage your participation, the Sound Science forum isn't the right forum to post your impressions and suppositions of sound/music engineering as facts. If you don't know or are not sure, by all means ask.
G