sounds like your gauge is broken or there is a short in wiring
No, the regulator in the alternator only regulates when the alternator is charging (alternator must be rotating).
Yes and no you have to rebuild the gauges so they read 12 volt The volt meter wont work with an alternator it was designed for a generator The fuel gauge is different ohms if you stay with the 6 cylinder engine the oil and temp gauge will work but if not the temp gauge has to have a longer tube installed and the oil gauge has to have different fittings installed. on the upside though your speedometer should still work.
If your battery was dead and you jumped it to get it started and the gauge shows your not charging you need to replace the alternator.
It is common for there to be three temperature sensors, one for air, one for the EFI computer and one for the gauge, so yes the sensor can fail and the gauge will still work because it is a different sensor.
That particular wire is usually 10 gauge.
why doesn't my rpm gauge and temp gauge, fuel gauge not work
Can be a defective voltage regulator.
in a series battery, alternator, ignition
on some vehicles the gas light will still work if the gauge does not. on some vehicles such as an 1985 Toyota cressida have a separate sensor allowing the low fuel light to illuminate.
Weak battery, or weak alternator.