did you do any work under the hood? maybe washed the engine bay? shake can be from many reasons, like engine mounts, or MAF sensor unplugged, or misfiring cylinders... the list goes on...

factory hitch is the only way to go, instead of getting a used one, go to a dealer - should be in vicinity of $1000 installed... too many parts involved in the installation to go used route...

amp... depending on the place that diagnosed it, the diagnosis might right, might be wrong... what are the symptoms? there are a lot of people here that can guide in the right direction if you want to get a replacement amp...