Faulty battery, bad alternator, or both (photos)

Good progress. I hope by now you have read the MADD article. This points out the problems with the bulkhead connector. Check it thoroughly. Now that you've had a BAD short, one that fries wires, there's been a LOT of current going "back and forth" (figure o' speech) through there.

Frankly, at this point you should consider dropping the column, pulling the cluster, and stripping the under--dash harness out, and at least PARTIALLY untaping it and inspecting it. There is probably damage----damage that can cause shorts later on if not now.