Though your system may be different, the pressure in the air tank is usually set to around 32lbs when the system is 'not in use'. That is, when the tank is installed or when the system is depressurized (pump off, faucet open). The pressure switch has a high and low setting which should be something like 30psi and 60 psi. If the bladder in the tank has a leak, water may burble out of the air valve at the top when you measure the pressure.

When there is more than one check valve on a system and the upstream check valve fails, when the pump shuts down water leaks out back to ground. If the leak is small, you will only notice the problem when the pump has been shut down long enough to form a vacuum in the line (because there is no way for air to enter the pipe). Then you get water hammer when the pump starts. Pull the pipe and replace the check valve.

I don't think you understand what the divices are supposed to do. The expansion tank's primary function is to prevent sudden spikes in pressure and resultant water hammer as faucets are opened and closed. The prv's function is to open in the event pressure in heater tank rise's to 150 psi. When the prv opens water flows into a floor drain or other area until tank pressure fall's to a safe level. Before the advent of prv water heaters expolded with enough force to take out walls,kill and injure occupants. You have too much pressure coming into the home and should contact a plumber about installing a pressure regulator. The wildly varying pressures you are seeing is likly because someone partly closed the main water supply valve in an attempt to control pressure. Call your plumber before high pressure burst's a laundry hose or sink supply and flood's the place.

The reason that you need to place the expansion tank on the hot water side of the water heater is because you will have a shutoff on the cold water side of the water heater. You want to avoid a situation where you have the cold water shut off to the heater, but because the heater is still on, it has no place to expand to. Putting the expansion tank on the hot water side solves that issue.