You only have one rear fog light. This is normal.
I think that you may be confusing the headlight running light and the actual headlight low beam(there are 3 bulbs in each headlight, aside from the fog light and turn signal: low beam, high beam, and running light)
The headlights should not come on with ignition off, only running lights. Each headlight has a small 3rd bulb which serves as a running light...my guess is that your left side headlight running light is out, but the problem could also be the headlight switch itself.
As a bulb is easier to check, I'd suggest you start with the headlight running light
Also remove the rear light assemblies and make sure that all of the metal contact strips are in place and have not popped out.
Then there is the parking light function...but that only applies to the switch in the "P" position(pulled out one position and turned one click to the left)