First off, the foot drip thing, my GS did this, so I had a look. It was indeed condensation drips. My pipes were lagged with a black foam/neoprene cover. Mine had a tear in it, and this is why it dripped. I gaffer taped it up, and it improved it, but did not cure it completely. So in answer to your question, yes, it should be lagged. I can only assume they started lagging the pipes at a later date, or your pipe has been replaced and they did not bother to replace the lagging.
Now the multi plug, thats an interesting on.
If your car is functioning fine, then its obviously not needed, but annoying isnt it. You can have cruise a cruise control stalk fitted to the steering cowling, and the wiring is all there, but if you put 2 and 2 together, I am going to take a punt and say its the wiring for the dash sunshine sensor. If the dash has been out and the air con messed with, then this looks the right plug.
If you whip your dash top off, you might get a better idea of what it goes to.
It could of course just be a redundant plug from the hifi or a service extra which your care does not have.
How many terminals does the plug have, I can see it only has 2 or maybe 3 wires.