The white wire isn't "hot" it's switched ground.
You do have an extra white wire and an extra orange wire. I don't know why, but these units were used in lots of makes and models.
Here's how the circuits work. You actually have two circuits sort of.
The dome light: The orange wire is always hot. That white wire connects to the door switches and the headlight switch. When the light is out, the doors are closed and the headlight switch is off. While the circuit has 12+ it lacks a ground so the lamp cannot illuminate. When you open a door or turn the headlight switch, the circuit is grounded and the DOME light will come on. Note that the map lights stay off. The terminals for the dome light are pressed into a plastic insulator that shields the terminal from the dome lights metal structure. This shields the circuit from unwanted grounding.
The map lights: The white wire doesn't come into play for this circuit. The orange wire feeds 12+ to each socket. There's a switch with a gray wire that also leads to the sockets. The switch is for grounding/ungrounding the circuit. When you move the switch, ground is achieved via the gray wire as the switch itself is grounded to the dome light metal housing. The metal housing is grounded to the body of the car. When the circuit is grounded, the map light comes on.
The light in your picture is slightly different than the ones I have which would explain the extra wires.
