No because water heaters have a safety valves and when the pilot light goes out the safety valve shuts off the gas
The gas will shut off and the heater will not work. Modern heaters do not have a pilot light but ignite the gas each time it is needed (this saves on gas).
A small amount to keep the pilot light going.
You don't. If the heater has an electronic spark, then it doesn't have a standing pilot to light. The spark lights the pilot when there is a call for heat, which in turn lights the burners. If the heater is on and the pump is RUNNING, the heater should light automatically when the water temperature is lower than the heat setting.
If the pilot light is on, the heater should come on by itself. If the pilot light is off then it has to be lit. If it will not stay on, the thermocouple is bad.
Have you turned the control from Pilot to On? Have you increased the temperature setting?
Yes
Gas water heater has an orifice for main burner and for pilot light, if not electronic ignition.
The water continues to run into and out of the water heater. There is just no flame to heat it up.
THERMOCOUPLE or defective gas valve
small amount
Same as any hot water heater. Turn the gas valve to off.
is the lines on the thermal coupler and pilot light for a hot water heater supposed to get hot
No, it is not dangerous. (Unless you are working with a water heater that is 20+ years old.) In any modern hot water heater, if the pilot light goes out a fail-safe will go off - preventing gas from leaking out. Also, there is a sensor so if there is not enough air-flow or oxygen with the water heater, it will shut off the gas.