Working Tiles: Can I Change Them?

You have to enter the city screen. Green icons are tiles being worked, black are tiles not being worked. Just click the icons to move them around. When you move them manually they will lock to that tile.
 
Yes. Open the city view, and in the top right hand corner is a "Citizen Allocation" button (a '+' button) Click that to expand, and you will see that the city center gets covered with green and black circles. Green = tile being worked, black = not worked. Click on these to change the tiles that the workers are working.
 
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