Some of your values are off.
10b = 75% (-25%)
15b = 56% (-44%)
20b = 34% (-66%)
25b+ = 10% (-90%)
Tax Rate Morale Penalty
30% = -32%
40% = -46%
50% = -65%
60% = -83%
70% = -107%
80% = -123%
90% = -176%
100% = -199%
I have taken those numbers straight from the game. If you did too, then please make sure, that you are running the latest version (v2.04).
5 stock exchanges = 5 x 25% = +125%. 16 bil +125% = 36.
Therefore, for D to beat A, it would need more than 36 billion pop.
Your conclusion is indeed correct. However, your calculation is not quite accurate. The tax income of your planets increases by the square root of the population. So, in order to gain 2.25 as much money, you need to increase the population by a factor of 5.0625 (the square root of 5.0625 is 2.25). In other words, you would need a population of 81b in order to make as much money as with a population of 16b and 5 stock markets.
70% is the absolute lower approval limit if you don't want to risk losing the elections.
You only need an approval rating of 70% or higher during election week. The rest of the year, you can run your tax rate as high as you want. However, I'd try to keep the approval rating in the yellows. Otherwise, you risk loosing some planets to revolt (they form their own little empire). I had that only happen in one of my games in all the years of playing, but it is a possibility. Even so, it didn't even happen to me, but the Iconians, who were running their economy to the ground.
Problem with any government: unhappy planets easily join/create breakaway races such as The Jagged Knife (which none of my planets do since I noticed that).
Not necessarily. I lost planets with an approval rating of 90%+ to the Jagged Knife before.