>1. A difference of 3 in dB means times 2, a difference of 10 means times 10.
How can this be right? Aren't you kind of fudging it a little?
Here's my train of thought:
First I was thinking "What the hell is going on with your math? There's no clear factor to turn base 2 into base 10 what the hell. How can what you say be true? How does this work?"
My next thought (based on your incorrect statement) was, oh, they didn't choose base 2: they chose every 3 to be another factor of 2 - so let's see why that works, why +10 is the same as * 10 if every +3 is * 2. Well, you can get to 10 by going 3 + 3 + 3 + 1 and you can also get 10 by going 2 * 2 * 2 * (1.25) = 10.
Okay, so if every +3 converts to * 2 then why exactly does the last term, +1 convert to * 1.25?
I thought, and thought about it. I couldn't make it work, based on your rules. So I checked. And the answer is it doesn't: 2^(1/3) isn't 1.25 as we would expect, it's 1.2599. That might seem "close enough" but I think it's not exactly how you say and your statements are misleading.
Thus 23 dB isn't 200 times stronger as you state (23 = 10 + 10 + 3), it's only approximately 200 times stronger. 200x stronger is 23.0103 dB, and 23 dB is 199.52 times stronger. [1]
While it's useful, and the error is pretty small, it doesn't help for those of us used to thinking in terms of bitfields or something that converts quite exactly.
It's definitely a very useful mental estimation trick though!
[1] which I checked with an online calculator here - https://www.rapidtables.com/electric/decibel.html (first I entered a level of 200 and clicked the top "convert" button, then I entered a dB of 23 and clicked the second "convert" button)