What’s the relationship between gain (dB) and power (watts)?

With all the math and physics measurements being tossed around, you’d think that everyone was equally gifted with identical hearing and processing by their brains. Unfortunately, this is not true and varies again by the condition and training of the listener and by their age. This is what makes "audiophiles" out of "just another person, but gifted by the Lord with perfection and the ability to communicate perfectly." I hope you are laughing at how arbitrary the listening experience can be. The most important aspect of the whole thing is how much you enjoy the experience of recorded sound and music.
I have a degree in experimental psychology and have been an electronic design engineer and owner of a graphics/media company with a recording studio for over a decade. This is irrelevant as I ENJOY music and have for a long, long time.

This discussion is getting out of hand as simple DC models are being compared with exotic AC ones. The math is being dumped out of a need for a model of understanding which doesn't match the challenge of the questions. The answer to all of them is... the questions are too difficult to separate into little pieces. The basics are just that, basics. The answers are beyond the understanding of most people because they encounter ideas such as statistics and psychology, which some people think do not "fit" into any discussion of music. However, they do... as well as other areas of mathematics and exotic theory, both electronic and as apparently "simple" as component design (so sorry, that is ALSO extremely math oriented). The bottom line is, most people simply cannot, will not, and don't either believe or know the answers. That means if they are right or wrong. Good luck.