1) Do you have the Kremlin? If it actually expanded to a new tile that wasn't previously part of the city, then the Kremlin is usually the only way that happens. (if not: bug)
2) The game will notify you when you have expanded culture, which includes when you have captured their cultural area. It will also notify you of each tile where culture expanded that you cannot work, if that occurs when you capture one of their cities there can sometimes be a lot of them in the later game. That's a feature if that's all it does. Actual expansion is a problem.
3) I'm pretty sure it isn't notifying you of actual population growth, but rather that it has a new population (it will notify you everytime a city goes down from starvation/razing as though it grew as well). It very probably went down in population. If it went up, that's a bug.