You have to remember that *where* along the signal path gain is applied, has an effect on noise. And therefore turning the iso dial, really affects snr, and hence really affects the iso by definition.
It's very easy to see even experimentally why *where* you apply gain plays an important role. Take your phone, a headphone amp and some headphones. connect phone-->amp-->headphones. Then try
1. phone volume at 100%, amp volume at 50%
2. phone volume at 50%, amp volume at 100%
Is the noise the same? No. (unless phone and amp have the exact same amping circuitry).
This is where you should start to avoid any confusion. Wrt your points>A.
A continuous dial is very possible, and a matter of firmware and to a lesser extent hardware. Maybe it exists already. Also there are no iso invariant camera bodies, for the reason I explained. And that's why adjusting the exposure slider in post *is* different - you're applying gain at a different point in the signal's path.>B.
They follow it closely enough. There was even more wiggle room with film. ISO would be specified for a specific developer, dev time and agitation, and contrast index. You used a different dev with lower base fog? Your iso just increased. You used a dev with more upswept curve? Your iso just increased. Etc etc. A bit of leeway is not a huge deal, people were able to work with "leeway" of 2 stops with film depending on developer, half a stop leeway in digital is unremarkable.>C.
Or use gain at a different part of the signal path (i.e. turn the iso dial). Or cooling your camera's circuitry to reduce dark noise, hence increase SNR. But aside from that, yes only a different sensor will give better snr. Just like with film, after you exhausted different dev techniques, only a different film would give you better SNR.>D.
It's a bit more complicated, not just photosite area. But also quantum efficiency, dark noise, etc. etc. . But yeah, all things being equal, yeah.>E.
Photons *per area*.