That battery is currently
very dead! A flat battery will naturally reduce the net system voltage when it's connected to the alternator but I suspect that your alternator is also bad.
I would first charge the battery fully so that it's not part of the equation. Once it's charged, check its voltage under load - turn the radiator fan and lights on. You should still see 12-12.5 volts. Less than that indicates a bad battery.
Next, check the voltage regulator. Make sure that the case is grounded through the black wire. Use
this guide (page 8) to bypass the regulator.
I suspect that the alternator is cooked.