Yes, the dimmer switch should turn on the dome/interior lights when the doors are closed. When the switch is rotated all the way to one side, there should be what feels like a bump or perhaps better said requires more effort to turn the knob (its noticeable), this connects the dome/interior lights and turns them on. Those switches can and do go bad mainly from being rotated back and forth. Many times they can be cleaned up and reused, other times they need to be rebuilt or replaced. Also to your question, as you rotate the knob it should dim the dash lights.
As to the 2 black wires in the front, you are probably correct that they are for your road lamps.