1. You are correct, you get the base of the tile as city center, so without features, with the minimum being 21
1
. The forest doesn't count. floodplains is a little wonky, as it counts as a desert tile, so settling there would still only get you 2
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For what it's worth, the reason floodplains is wonky is that Civ treats floodplains as a feature - like forest or jungle - which is therefore destroyed if you put a city on it. You can see this if you ever capture and raze a city that was built on a floodplain - you'll find what's left is just a plain desert tile. Seems a bit unrealistic to me - I can see how a city would destroy a forest, but not a floodplain. But it's how the game works

2. The Fur is on an island, so even if you were to settle on the deer (which I think is a really bad idea), you can still settle in a comfortable position on the island, because you can settle only 2 tiles apart on different land masses. Quite often this can be the case with a 1-tile island off your starting continent.
Agreed. I think in my case, it's partly because I have an aversion to putting cities so close together. But then, I almost always play for space, which means I spend a big part of the game with all core cities at 20+ population. Cities having their growth stifled because they share so many tiles probably doesn't get nearly as annoying if you're going for domination or an earlier victory so your cities never get that big!