In relpy to number 3, I take it you mean what we call the tailgate, the door at the back that gives access to the boot space?
I've just had a look at mine and as you say there is a switch, off/auto/on. Mine was set to off when I got the car, so I switched it to the auto setting so it came on when you open the tailgate. Then I thought the reason why they might have it off. If you're like us then you might have the tailgate open some time, we use it for sitting in the boot area when out for the day, putting walking boots on, sitting when having a picnic etc, all things which could flatten the battery if the light was on the auto setting.
Anyway, getting back to the point, I've just had a look at mine, and providing you have the switch on the light set right it should open when the tailgate is opened. I've looked for the switch and it appears to be inside tha tailgate and is operated by the lock latching. If you try closing the lock with a screwdriver (don't close the boot while in this position), the light goes out. Pressing the boot lock relase button sets the lock back to open, and the light comes on.
So I'd say the light is working ok, it lights up when set to 'on', it looks like the switch on the tailgate lock is stuck in the off postion, and not releasing when the lock opens. You should be able to get at it if you take the trim panel off the inside of the tailgate, and maybe try freeing the switch with some penetrating
(WD40 type thing). If not it sounds like a new switch might be needed (you maybe lucky and it's just a bad connection on the switch or a loose wire).