My alternator wire melted.

Unfortunately new does not always mean good. Sorry to read about this.
Since turning the ignition off did not kill the power to the fire, at least one failure was the battery feed shorting to ground inside the alternator. Fusible link should have gone first, so maybe other things going on as well. (see example Fusible Links in Charging Systems with Ammeter)

On your alternator - regulator setup, the green wire goes to ground through the regulator. That's how those regulators control the voltage.
67dart273 I think covered the rest.
I have a 1971 plymouth scamp. I was tuning my carb after a cam swap when I noticed flashing coming from inside my alternator then my engine died and white smoke was pouring out from the harness. Even with the engine dead it kept burning until I disconnected the battery. The blue wire that plugs to the alternator field melted all the way to the firewall plug. It splits off to the voltage regulator but that wire didn't melt. The green wire that comes out of the regulator that goes back to the second field had broken strands at the connecter and broke off after a couple of wiggles. I also found corrosion inside the firewall plug. So I'm thinking it must be one of the two that caused it but not 100%. Anybody have input. BTW it's a new alternator with 2 engine hours on it.
The blue wires are branched off the "ignition run" which IS NOT FUSED. That IGN1/ run feeds several items depending on year / model

Feeds power to ignition system
to VR
to alternator field
to electric choke if used
emissions doo dads on some years

MOST LIKELY you have a short in that blue wire or right IN the alternator. The two field connections at the alternator should show continuity between the two of them, but NOT to ground (case) of the alternator

You will be lucky if you didn't burn up "some other" wire. I would get under the dash and try to trace the "ign1" where it comes out of the bulkhead and goes to the ignition switch.
Wouldn't you know I read straight to ground on fields 1&2. Now my question is that why the wire melted? Would a short somewhere else cause the short on the fields? To recap, engine running, notice flashing inside alternator, engine dies, wire starts to melt, (with ignition still keyed on) stops melting when I disconnect battery. One more thing, voltage regulator mounted on firewall reading from regulator case to ground was not constant.