I think you probably have one or more problems at play here and it's difficult to know what to suggest next. You have a wire that has burnt out in the loom without blowing a protective fuse, which is unusual. It may well have damaged other wires in the loom and perhaps the ECU itself.
I think I might be inclined to take the engine loom off the car, try and get a replacement one (and maybe an ECU too if you can get one for a sensible price, but you'll need to reprogram the transponders in the keys) from a scrap car then go round every ancillary in the engine electrical system and check for shorts before firing it up with a new loom and, perhaps, ECU.
Have a look at all the fuses as well, and make sure they are the correct values. The fuses should be rated to protect the wires in the loom, preventing this kind of problem, so maybe someone has had a troublesome fuse that's been blowing in the past and has replaced it with a higher rating
It might be worth trying the ECU in another car just to see if it is intact but don't plug a known good ECU into this car until all the wiring has been replaced or thoroughly checked.
Another thing: Have you tried measuring the battery voltage when running at a fast idle? It's possible the regulator in the alternator has failed causing an excessive supply voiltage and this has caused multiple failures in the electrical system. Might be why the alternator light is flickering.
Edited to say: Another thing to try. Check all the earth connections between the battery, the body and the engine block.
Kevin