The thermocouple is the small tube that runs between the pilot light and the control valve. The valve end unscrews and the pilot light end in held in place with a spring clip that the tip pushes through. Unscrew the valve end and work the pilot end out by twisting it and pulling it out of the clip. Install a new one making sure the end is in the pilot flame and light the heater. No gas will come out when you take it loose from the control valve.
"How much" as a question is quite vague. Some hot water heaters are comprised of copper only. So this now depends on the size of the hot water heater. Some hot water heaters have no copper whatsoever.
Check the temp on your hot water heater, you can turn it up.
Because you're in it.
The elements possibly.
Tankless. A tankless heater heats the water as you use it. It doesn't store hot water and keep it hot day and night whether any is used or not. The water is heated almost instantaneously, and the heater will keep the hot water flowing as long as the water is turned on.
There are many pictures of this on Google.
$6 to $10 depending on where you are and where you get it from.
THERMOCOUPLE or defective gas valve
Sounds like you need a thermocouple.
You do NOT clean a thermocouple. They are really inexpensive and when they are giving problems have a LMP / or Gas fitter replace it
Spillage excessive condensate bad thermocouple draft
Depends on the age of the heater. If you light the pilot with a match, you should be able to remove the thermocouple with the burner in place. The end that is in the flame will pull out of the clip that holds it. The control valve end unscrews. If you have a newer one that lights the pilot with a sparker, you have to remove the burner as a unit. There should be two screws holding the cover plate in place, the gas line to the burner, the thermocouple and the wire for the sparker. Disconnect all of these from the control valve and the unit slides out through the hole. Then change the thermocouple and replace.
Most pilot lights are not adjustable. If it's not working properly the usual solution is to change the thermocouple.
The thermocouple is going bad. The thermocouple is the small tube that sits in the flame from the pilot light and goes back to the gas valve. They are easy to replace and cost $6 to $8. For health and safety the failing part should be replaced without delay by a competent gas engineer.
Follow the attached link -
All countries have rules and regulations, only a qualified plumber may install, replace, maintain a hot water heater. Therefore the permit required would be the plumbers qualification
Replace the shower valve.