Sounds like your main line coming in is small if it's 1/2 inch stepping it up to 3/4 coming in then down to 1/2 inch would increase your pressure
This is probably a pressure imbalance problem or you have air in the lines. see the related video link provided.
Your local building department and the Plumbing Code, a normal test for a water system is to prime the system at the pressure it will be running, as long as it's not above 80psi and checking for visible leaks and pressure drop or meter movement.
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.
No, cold water is piped into the hot water tank and is heated by electricity or gas, it then flows out to the hot water taps.
the hot water valve shut off valve shuts off the hot water. The cold water valve shuts off the cold water. ;()
Pressure is the same whether hot or cold.
This is probably a pressure imbalance problem or you have air in the lines. see the related video link provided.
There are several possibilities. The 2 most common would be the water heater needs replacing, or you need a repipe.
Possibly a frozen line huh?
Lots of stuf can cause it including sediment or a blocked supply line
Hot or cold?
water pressure
Install on cold water line.
Ones hot and ones cold.
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.
More than likely it is restiction in your water heater.
Cold water is denser then hot water and weighs more so hot water will always stay on top of cold water no matter the pressure in the line or volume unless forced by flow hot water water will always be on top.