Okay so this should be a simple question. Does it make a difference if you bolt down (with the provided C clip) the ground wire along with the parking brake for the Mod and the Mute wire for the Mod to a ground or can you just hook them up to the ground wire that comes out of your factory harness adapter? I know a grounds a ground but i want to make sure that i don't introduce any noise to the system.

either way is fine

Either way will work, but it's usually better to ground them all to the car. Some car's supplied radio ground wires aren't all that great. At least this way, you can be sure.