[flashollie]

I had a E61 series touring til last month. They had a notorious fault with the wiring loom to the rear tailgate.
The 2 cable bundles through the hinges to the tailgate were far too tight and not of a high flex type cable.Over time the cables become brittle and go open circuit or worse the insulation fails and they start shorting across each other giving all sorts of weird faults.
The fix is fit new loom from within the roof mounted speakers. Not a straight forward job but Quarry motors did it for me for a good price. Dealer was after about £700 per side I think.

Now I'm in the F31 club I don't know if this is a common problem on this model or not but some of your symptoms are similar to what I had on the E61.