The previous owner may not have re-installed the wire harness for the hatch. It doesn't disconnect at the roof, it's all one piece that has to be pulled through the hatchback when removed and fed back through when installed. That's my best guess considering your rear wiper is inoperable as well. Worst case scenario they cut the harness to make the job "easier", or the pinched the harness causing a short to ground. Removing the lower and right side interior trim panels from the hatchback will give you access to the wire harness for inspection.
As for the water leak, inspect the hardware for the rear bumper crash beam located in the hatch underneath the rear carpet. There are four large bolts, two on each side. If they're loose or missing, water will leak onto the underside of the carpet. Also remove the rear side trim panels to inspect how bad the quarter panel rust is. Water will be splashed into the top of the wheel well while driving and seep inside the vehicle. While the rear side panels are out, check that the power antenna is installed and secured correctly and that the rear moon roof drain tubes aren't damaged or clogged.
Looks like you're off to a good start. Good luck!