My guess is that the hot water heater is installed downstream from a pressure reducer to limit the maximum water pressure that the water heater is exposed to.
no you dont It is safe to leave the water on, whislt changing the stem If you don't want any problems, turn the pressure off.
Water expands when it is heated, this expansion increases the pressure. The bladder tank absorbs the extra pressure, protecting the hot water heater.
I would`nt... It serves no purpose. If the water is off there is no pressure when you turn on the tap, hot or cold, so you would be heating water you can`t use.
If you have an instantaneous hot water heater, and your faucet doesn't flow enough water it won't turn on the water heater. Thus requiring another faucet to be turned on.
Check the temp on your hot water heater, you can turn it up.
More than likely it is restiction in your water heater.
Generally this is caused by pressure being built up from the water getting hot in the hot water heater. By code you should have a hot water heater expansion tank on the cold water inlet of the water heater to absorb the added pressure. If this is your problem, the excessive pressure could possibly burst your water heater. The faucet stem or cartridge or washer may be loose or moving and blocking flow.
Same as any hot water heater. Turn the gas valve to off.
turn off your water
Only if installed incorrectly
It's not a bad idea to turn off the water heater especially if it is electric. It will consume power the whole time you are gone to keep the water hot and wastes a lot of electricity.