The black box on the engine should have three large wire connections (in addition to wiring
harness connections). The center one is +12V, to one side is the orange glow plug
wire, to the other side is the starter solenoid wire.
The relay inside the black box can be frozen, or the switch at the panel can be stuck, or some connection between the panel and the engine could have a short. Easiest way to check it to put a voltmeter on the orange wire, then disconnect the wiring
harness connectors from the black box (the ones that go to the instrument panel). If the glow plugs stay on then the problem is a frozen relay. If the glow plugs go off with the harness disconnected then the problem is a short at the switch or in the harness.
On the alternator side of things, the yellow sense wire is only really needed (and will only really make a difference) if there are some losses between the alternator and the battery
(like a diode separator). If the yellow wire becomes disconnected the regulator
controls to the voltage at the alternator output terminal. If there are not many losses then that is pretty close to the voltage on the yellow wire (and it is the original harness, and you have not connected the yellow wire direct to the house bank then it is really the same voltage). I suspect the two problems are not related (other than belonging to the same green engine).
Here is the wiring diagram,
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The red wire is +12V, the orange runs the glow plugs, and the red/yellow runs the starter. Since the switch on the panel does double duty as both start and pre-heat it is, IME, not usually the problem. Instead the relay inside the MDI gets stuck.