They're not supposed to, but aren't we talking about a bug?
Yea but city level remains. Number of usable spaces remain. And population amount remains unless it was houses that vanished in which case it only drops if population was at cap.
There was a bug before when cities leveled up they would drop some population right after level even if they had plenty of room. That seems to have been fixed in 0.302 as city pop is what you'd expect for a city that just leveled up. Plus buildings only disappear when town levels up or new R&D. Haven't gotten them to vanish any other times even when I recruit the whole city into the army.
On a side note you can build town halls in level 2 cities and not just "towns". Guess I should add that to the bug report. But it's a good thing you can cause it would take forever to reach 250 population needed without the town hall's prestige bonus now that leveling up the city doesn't give a natural prestige boost.