warning lights and engine problem

I have a 2002 Ford Taurus and:
1) 3 warning lights  (Engine, Doors Ajar and ABS) stay on after the engine starts, but
they will turn off if I turn the head lights on.

2) The engine will stay running if I turn off the car and remove the key; but it will shut
off when i turn off the head lights.

Is there a "normal" reason for this?