Hello, for the symptoms you describe, I think the problem is on the alternator's pulley. This one carries a Crickt system (similar to the pinion of a bicycle, to the one side- for the other, no). If the Pulley Cricket system is worn, increasing the load, skate, preventing the battery charge, which is exhausted by the consumption of the injection system + accessories. On the other hand, the tachometer has the revolutions from the alternator, which explains why the needle goes crazy.
Good luck, and greetings from Córdoba, Argentina.