There should be a spring under the thermostat housing that holds the thermostat against the horse shoe shaped spacer and rubber thermostat seal. If any water is leaking past the thermostat seal, you may get a low reading.
If everything looks OK, I'm not sure I'd worry too much about the temperature at this time of year. Considering the incoming water temp was low, what you're seeing might be normal. Since the cooling system is not a sealed pressurized system like in a car, it's not going to behave exactly like what you see in a temp gauge in a car.
The most important thing is that the motor is not over-heating.
As far as the tach issue...did you check it right at the new regulator, or were you using any of the existing wiring harness.
When ever I install the regulator that has the two red wires, and the wiring harness only has a single connection, I always tie the two red wires from the regulator together. Don't know if that makes any difference. I would think that they should be the same.
As far as the charging voltage, you won't see any increase in voltage until the motor gets up to about 1500 or 2500 RPM for about 5 to 10 seconds. Then you should see anywhere from 13.5 to 14.5 volts DC at the battery. If you are seeing just fully charged battery voltage 12.5-12.7 volts DC while at 1500 to 2500 RPM's, then I would suspect the charging system is not working. Either the charging voltage from the stator to the regulator is not good, or the regulator is bad.