I have a few general questions.
How come sometimes you can't request another civ to change their civics? In one game, I'm running central planning, but I can't ask my vassals to switch to central planning, or any civic for that matter. I know that they have the required techs.
Similarly, how come sometimes I can't trade a city to another civ? The list of cities doesn't even appear in the trade menu. I can trade cities to some civs but not others.
On a side note, is it correct that there is an outdated penatly for all organization civics other than totalitarianism and egalitarianism after you discover communism? It has nothing to do with central planning which is the civic unlocked by communism. If you research communism before fascism, then the only choice is egalitarianism. It seems like representation should be acceptable at least until fascism is discovered.
How is the stability penalty for losing wars calculated? I was fighting multiple wars, but I believe that I was winning the wars as I was able to sue for peace with things added on my opponent's side of the trade.
Finally, in my attached screenshot, what does the column with the red circle represent on the city info screen? The values are 12, 10, 10, 9, 9, etc.
You can't request a civ to change its civics if it has changed in the recent past. It works the same way as for you i.e. a couple of turns after a revolution, you can't change civics.
You can't trade away your cities to your vassals. The only exception is if it causes revolts, I think. (However, I agree that you should be able to trade away core cities, or your vassal shouldn't collapse due to that. Maybe core cities held by master should count as vassal's for vassal stability?).
The penalty for central planning makes sence. If you are forced to live with outdated civics, then wait some turns more. Historically, communism was adopted 70 years after it was invented.
The war penalty is based on war wareness AFAIK. Even if you win your soldiers want to go back to their homes, and they don't want to die in the field.