12.06v on the battery is seriously discharged (probably due the system not charging because of to the bad regulator); a good, well charged battery will read 12.6-12.7 volts, after it has been taken off the charger for a few hours, or you stop driving for a few hours, and check the voltage afterwards. Don't check the battery voltage right after driving or taking off a charger; it needs to 'rest' to reach a stable voltage.
With 12.06 volts on the battery, then it is either:
1. Heavily discharged and the ammeter swinging hard to C is normal as the alternator is pushing current into the discharged battery as fast as it can. You would expect the ammeter indication to start moving away from C and towards to middle more and more as you drive it more and more, IF the battery is basically good and was just discharged. After 30-60 minutes or so, it out to settle in near the center.
2. Or the battery is bad in a certain way (shorted or partly shorted cell) and won't hold a good charge. If you charge it overnight and then remove the charger, leave one terminal disconnected, and let it 'rest' for a few hours, and then measure the battery voltage, it should hold at around 12.6 volts. If it has dropped or is dropping after 'restring', then the battery has a bad cell.
The ammeter will only be in the middle if the car is off, or is running and the battery is fully charged. The ammeter is there to indicate current flowing in and out of the battery, not the current in the rest of the car. So if the battery is even partly discharged, then the ammeter will indicate in the C range to some degree depending on how discharged the battery is....