Water – Frozen water lines, what should I do with the electric hot water heater

The click-click-click sound is probably coming from the water meter.

Check if it makes the same sound when you run COLD water, in a kitchen sink, for example.

Sometimes a mixing valve is used to put some hot and some cold water into the toilet tank to prevent or limit the tank sweating in the summertime. The mixing valve is adjusted to "temper" the water by adding just enough hot water to raise the temperature of the water in the tank from cold, to I'd say "lukewarm", but not hot. The water is then much closer to room temperature, so it won't "feel" hot, or even particularly warm. If a mixing valve is installed and the water feels hot or even particularly warm, or even on the cold side, the valve needs to be adjusted.

In either case, cold water only, or a mixture of hot and cold, some water meters just "click" as they measure the amount of water flowing through it.

Since you have a flue I assume it is either gas/propane or oil fired. Most water heaters have cover near the base to service the burner or the igniter. First shut off the fuel source. If you remove the cover you should be able to look inside with the aid of a flashlight. Most burners are round and you may find that the cap has fallen into the center and may even be on the floor under the tank.