When I had my Legacy there was one time where I was power washing it and a huge chunk of paint came off the rear quarter fender. I learned just how bad the paint was after that...
Definitely sounds like the alternator for sure. At that point with the age of your battery, I would consider changing it along with the alternator to be on the safe side.
It's honestly the best way to go. Granted my car still has 3 years left of payments but it was best for my situation. I plan on getting a used truck for cheap in the future to run along side my primary vehicle.