There is no solution within the scope of the rules you posted. You can't use a cylinder or a sphere to make it work, either. You could probably use a torus, but then going into 3D would open up the possibility of saying that the phone lines are on poles and the water and power are underground.
As for the last puzzle, you can do it with one continuous line with no turns if you wrap it around the globe. If the solution must be planar, you could draw three lines.
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351W 89 Mustang GT Convertible