What was logic behind Ford wiring it that way?
Fog lights are supposed to be used in the fog, and "running lights" are also required to be on. To wire fog lamps to do that, Ford "tapped" into the regular headlight circuit in the simplest way.
When I turn on fog lights , ammeter/oil pressure lights and interior lights come on. Is that common as well?
Same as above. Both my 65 GT and 66 GT Mustangs are wired similarly.
What is strange is my Lucas lights don?t work?.. no power to lights.
Sorry, what Lucas lights?
An electrical assembly manual would be a great help to you in solving some of these problems.
That's an understatement. Get a full set of Mustang Assembly Manuals.
Jim