You MUST replace the burned wires. Do it one at a time, using solder and shrink tubing. I've seen entire wiring looms smoke out and even fry components when left with bare exposures.

Your late model is dependant on many electrical inputs to operate correctly. Your high idle might be induced by turning on your A/C. Your ECU sees this as an extra load and compensates by increasing your idle speed. In gassers it's done by extending the impulse time to the injecters and increasing timing at idle by a couple of degrees. I'm not sure how it works on newer diesels.