Water could be too hot and goes through a tempering valve that adds cold water to bring it down to 120° for the home ? my guess never seen one .
. Cookie
The cold water pipe is to let water into the water heater tank.
I believe the coil inlet and coil outlet are for a coil inside the waterheater tank. The water, to be heated in the water heater, comes in the cold inlet and out the hot outlet and is heated by the water from the boiler running through the coil.
In a one story house, the water pressure in the boiler is regulated down to 10-14 lbs and is totally separate from the domestic HW which is at street or well press.