Welcome to the forum.
No, it's not normal for the PT to shake or have a vibration but it does sound like the plugs or wires are past their limit and breaking up. It's a major cause of hesitation, stutter, and ruff idle. If you can do the work yourself, it's an hour job following the instruction on this forum and the cost of 4 spark plugs and a new set of wires.
The other things you describe with the tail lights do sound like it's been hit in the rear. The lights are sealed except to where the bulbs go in and they have a rubber gasket to make it almost water proof so air is getting inside which means the seal is broken somewhere around the light. It should also be a tight seal between the bumper and bottom of the light so the fascia might have been replaced or repaired.
P.S. I almost flipped when I saw the price of that cruiser $47,000
But I guess your dollar isn't exactly equal to ours. For a little less than that price I'd sell you mine (perfect shape) and even deliver it to you in person.
