I was just in there yesterday. I used the switched power and ground off that existing plug for my Audiovox Cruise Control (my thanks to Roy Bertalotto). If I was putting heated grips on (and Im not) I would have used that existing plug. I dont see why you wouldn't use it, that's what its there for!
As for removing the tank... its pretty easy really. First, get a good thick blanket or something to place the tank on and lay it out (think ahead!). Remove the seat.
You have to loosen or remove the attached fairings around the tank area. On your question about the fairings, you will need to take off the pieces at the very front/center of the tank and, the two L-shaped black pieces bolted to the sides of the tank. The big pieces of fairing just have to be unbolted from the sides of tank.
Remove the big bolt on the back of the tank. The tank hinges up, the hinge point is at the front. There is a metal bracket under the rear bolt that is used to prop the tank up. The fuel and power connectors are under the rear of the tank, they quick-disconnect. Last, remove the long skinny bolt on the front of the tank that acts as a hinge. Lift off the tank and put it on the blanket you had the foresight to place on the floor nearby.
Hope this helps.