The answer to how much electrical power the alternator produces is ALL OF IT! If you "borrow" some charge from the battery during cranking or slow idle, the alternator replaces that charge when the engine is running faster. In the meantime, it is running the ECU, the fuel pump, the cooling fan, the radio, the running lights, the AC clutch&fan, etc, etc.
An alternator(at speed) is a current amplifier Iout=k*Ifield, where k ≈ 25, i.e. 2A of field current makes 50A of output current.
The Voltage Regulator watches battery voltage, and controls the field current to make the battery voltage a nominal 14.4V. If you turn on your 20A headlights, the battery voltage would sag slightly, the VR sees the battery sag, it cranks up the field current, the alternator puts out more output current to just balance the added headlight load.
Due to the field inductance, it takes the alternator about a 1/4sec to respond, so when a big load is addec suddenly, during that 1/4sec, a little charge comes out of the battery. As soon as the alternator output increases, it carries the total load again, with a small extra amount to replace the charge that was just borrowed from the battery. At the end of the day, the alternator produced ALL the energy that was consumed, because the state of charge of the battery is maintained.
My Cessna has the traditional zero-center ammeter in the positive lead to the battery. At slow idle, if all the lights, radios, avionics, pitot heat, etc is turned on (total load ~50A) , the alternator cannot keep up with that much load, and the ammeter will show a net discharge of 20 to 30A.
If you rev up the engine, the alternator speeds up, and can deliver up to 60A. At that point, the ammeter shows a net charge of 10A, because the alternator is supplying the 50A of load, and there is 10A left over to recharge the battery. The ammeter stays on the charge side while the battery regains the charge it gave up while the engine was turning too slow. It gradually tapers to zero, indicating that everything is back in balance, with the battery nominally fully charged...
If the alternator fails (or you turn it off in flight by pulling the field breaker), you immediately would see the total current consumption of the entire aircraft as a discharge on the ammeter. In the event of a failure, it is up to the pilot to react by shedding unnecessary loads, and by landing as soon as practical.
An accurate digital voltmeter monitoring the battery/main bus voltage will also tell you if the alternator is carrying ALL of the load, or if some load current is coming out of the battery. If the battery voltage remains at the nominal VR set-point voltage (say 14.4V), then you can be sure that no current is coming out of the battery (some could be going in).
If the engine is at idle, and the load exceeds what the alternator can produce (at that rpm), then you will see the battery voltage sag below the VR set point. As the engine/alternator speeds up, you will see the battery voltage come back up to the VR set point, at which point you can be sure that the alternator is carrying the total load, with some left over for recharging the battery.