Concerning the alternator output, there are a few things you can do to isolate the issue. First off, remember that your external regulator adjusts the alternator output via the field voltage (which is typically a blue wire). The voltage value on the field varies but should be around 12V when the batteries are half-empty. Measure the field voltage output on the external regulator and at the alternator. Make sure the voltage is the same at both ends of the field wire.
To test the alternator, just run a jumper between the positive alternator post and the field post. This way you'll confirm that when the alternator receives 12 volts on the field post, it can produce current and will consistently do so. Once you isolate the issue you can further diagnose as to what is happening within the alternator or regulator.