Engine stays running without key in ignition (and more!)

Hey folks, back from fighting fire in Oregon
beer-gif.gif Did that once - in Idaho - I got a pretty easy assignment - structural protection. My hats off to you and anypone with a red card right now.

replace the damaged gauge wires
Assess that one you can take a better look. From the photo above only looks like damager to a portion of the insulation. IF SO, I'd fix that and not replace. Second option would be to splice in a short length. The reason is those factory ring terminals are generally very well fitted and insulated for that job. If they're damaged, then that's another story. If you do add wire, keep the length clsoe to original making allowance for the loss of flexibility at the splices.
Inline wiring splice clips........from the Dodge RAM service manual

1) I read somewhere that it is wise to use wire that is specific to automotive applications, as it is made to withstand vibrations, etc. Is that true?
Compared with house wire? Yes sure. Automotive wire is always stranded.
Under the dash, General Purpose automotive wire is sufficient. Sometimes its labeled primary wire.
There are other stranded wire grades that have more density, flexibility, and/or insulation that is more resistant to heat, oil and gasoline.
In the engine bay I often use marine wire or a SAE with a medium wall insulation.

changing RPM. More specifically, the needle moves to the charge side (right) with increased RPM.
Two possibilities:
1. Battery is low and the alternator is maxing out at slow idle. When you raise the rpm, the alternator can produce more power and the battery is sucking up that additional power. Make sure the battery is fully charged (use a charger) and see if this goes away.

2. The regulator isn't regulating properly. Two directions to investigate here:
a. Has the brush from the rotor that normally is connected back to the regulator been grounded? If this happens the regulator can't control current through the rotor. It could be internal or more frequently, the green wire has been pinched against the body or the regualtor failed.
b. The regulator is sensing the wrong voltage. If the regulator is seeing less than 14ish volts, it will let more current through the rotor in an attempt to bring the voltage up. Check what the regulator is seeing by comparing the alternator output voltage to the voltage at a convenient location near the regulator's sense wire (Blue). Ballast resistor or the blue wire where it connects to the alternator are two locations that can be fairly easily backprobed.

but I'm starting to suspect the alternator. Thoughts?
Ok. Its possible that one of the diodes is out or one of the windings (there are three) is broken. This would cause lower output at all times, but most noticiable at low speed.

Here's where I would begin.
1. Charge battery
2. Start car and this time have a handheld voltmeter to make measurements in conjunction with reading the ammeter.
If when ammeter shows increasing charge the system volts go up above 14.8 or so, then there is a lack of regulator control. If so, then measure what the regulator is seeing, and go from there.