If yu do have 120# oming in, install a regulator to take the pressure down to 75 #.
120 psi!?!?!?
My city supply from the street is almost 80 psi, and I think that's WAY too high. 120 is downright dangerous! If I were you, I'd be shutting off the main water supply when I'm not home, just to be safe. Appliances and toilets just aren't rated to handle that.
From my research, 60-80 psi is "normal". Anything outside that is bad.
I installed an industrial, bronze pressure regulator designed for large buildings in the house, and regulate my pressure down to about 60 psi.
Also, as someone already mentioned, a water heater expansion tank is a must. In fact, I believe in many areas of the country it's now part of code. Most pressure regulators won't permit backflow, as far as I know, so if the water company has a regulator at the street, you need an expansion tank on that water heater.
The water company played on your ignorance when they told you their system is gravity feed. The fact that the water supply is gravity fed is true, but irrelevant. They were trying to get rid of you. Remember the code of "customer service": it's always the user's fault.
Most municipal water systems are "gravity feed". You know those big water towers you see across the skyline? Those are what provide you your water pressure. They pump the water up to the top of those towers, and gravity generates the pressure according to the height of the column. [It's done this way because the water reservoir provides a buffer between the demand side and the use side so the water pumps aren't dealing with a constantly-varying demand].
I was thinking your super-high initial pressure was caused by the water heater building pressure when heating the water, then releasing it when a faucet is opened. But that doesn't explain the low flow.
The first thing I would check is the thermostat on the water heater. If it's broken, and the heating elements (or the burner) is stuck on, then your water temperature is getting way too high (which causes the high pressure, which causes the T&P release valve to open). If the heater is sticking ON, you may notice EXTREMELY hot water, or even steam coming out when you open a hot water faucet.
After that, I agree with Bill's suggestion that there's a problem with the regulator out at the street. If so, the water company needs to come fix
their equipment.
There is a simple way to test whether the excess pressure is being generated in the house, or at the street. Shut off the water main, then connect up your pressure gauge. Open a faucet until the water pressure indicated on the gauge drops down to, say, 50 psi. Then make sure every faucet in the house is off and don't let anyone shower, wash, or flush a toilet. Monitor the pressure gauge for awhile and see if it climbs.
Since you've isolated the house from the supply, if the pressure rises over time then your problem is inside the house (and it's probably the water heater). If the pressure remains steady, the problem is probably not in the house.
From what I've read, there can be problems with municipal water supply pressure skyrocketing during the night, when demand is very low. To test for this condition, you can connect your pressure gauge at night before going to bed. Open a faucet to get the pressure to drop down to supply pressure (this will happen within 60 seconds of opening any faucet in the house), then close everything up for the night.
Check the gauge in the morning and see if it has risen. If it has, then there's something going on from the supply at night, which is a water company problem.
Like I said, I'm no plumber. But out of necessity I've had to do a great deal of research because my house was destroyed (literally) by a broken under-sink supply line that cracked due (partly) to excessive water pressure.
Excess water pressure is nothing to scoff at!!! It CAN destroy your home and everything in it, just as easily as a fire could!
Ryan