Bengal Tiger
Emperor
The production cycle happens in several phases. I can't remember what the exact order is, but the gist of it is:
-At the end of your turn, you maximize gold production.
-After your first build popup, you cycle through all of the cities and maximize shield production.
So if you were working, say, roaded gold on a river then switch it to a railroaded and mined iron mountain, you get the gold and the shields. It's generally looked down upon to do this, and a fair amount of PBEMs explicitly forbid it.
Oh you mean the citizens thing. I usually have the governor control them especially during war time. I find it tedious when a city falls into civil disorder. But changing production from an improvement to a unit is fine, right?