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What needs to be understood is how the game determines how much you get from the tile the city center is on. The city center will produce a minimum of 2 food 1 production 0 everything else, no matter where it is. If the tile yield exceeds that then it will get the higher yield. For a 2-1 tile with Wheat, the Wheat will give no benefit to the city unless the city builds a Water Mill for +1 food from Wheat, after which the city center will produce 3-1. If it was a 3 food Grasslands with Rice then the city would produce 3-1, increased to 4-1 with a Water Mill (do remember that a Marsh will be removed if you put the city there). For Stone, there is no building that improves yield the way Wheat has, so a 2-1 will stay that way. It can still be used for adjacency from the Hansa (as will any other resource you build on) and allows construction of Stonehenge.
Other kinds of resources obey the 2-1-0everythingelse rule as well, so if you have say +3 gold from a luxury the city will get that gold.