Thermostat turned all the way up,thermostat defective, thermostat wired incorrectly, heating unit wired incorrectly, fan or heat relay stuck closed are the things I would look at to start.
Take shorter showers, or get a tankless, "on-demand" water heater that heats the water as you use it.
You will hear air circulating in the cold air return (or return air grille) when the heater or air conditioner is running.
Because when your house is cold the heater automaticly turn on and when its the temperature is at the degrees you set it as it turn off.
Turn up the inlet gas pressure on the furnace to create more BTUs.
Water heater fan? I have never seen a "water heater" with a fan. Possible a boiler, hot water heating system. Assuming you are talking about a "water heater" in a house. Please give a little more information on where it is and what it is intended to do.
Car will make when running even if heater core is not burned out.
Usually not. If toilet has a mixing valve going to it so warm water fills toilet tank and toilet runs constantly, then enough warm water could leak out through toilet to possibly have an effect on water heater.
is a slow running fan heater going to give same heat as a fast fan heater if both 2000 running at
The fan will run continuously if the A/C is on or the heater is set to Defrost. If that is not the case then either the thermal relay for the fan is stuck closed or the engine is running hot.
You constantly need hot water
Not constantly, but it will kick on from time to time.
It could be because the child has an allergy to something in or around the house. my husband had a constantly running nose as a child and it was found to be an allergy to wheat (his mother fed him cream of wheat every am)