That overheating wire sounds like there's a short somewhere. Do you have a multimeter? The continuity tester is pretty handy for finding shorts. A wiring diagram (which you'll find in the tech wiki) will also help. You can also check the voltage of the system while it's running with a multimeter.

Is the charge light on while the engine's running? Assuming it's wired to the alternator it'll tell you if it's charging. (The light stays off if the wire's disconnected.)

As with anything it's a process of elimination. Start with determining if the alternator's working and if the battery's healthy. Then look for shorts, burned fuses etc. If you can't spot anything you might try pulling a single fuse at a time and seeing if the problem goes away (this will pick on particular circuits).

Re the alternator fuse, I believe there is a fusible link to the alternator, I can't remember where, DD is usually on top of that sort of thing.

Hope this helps.