Are you confusing District Spaces with the entire Tile that the District Spaces occupy? They are not the same. Common mistake, which I made myself initially. Just review the tile spaces breakdown and movement pages of the rulebook.
No, districts are only the space where you can take city actions right? However most of the maps already have permanent corruption spots in the district, so idk if the "end of the round" is only talking about physical tokens, or physical and permanent