In most cars, the fuel system should hold the pressure for quite a while. You shouldn't see a significant drop in fuel pressure after engine/pump shut off. What you are probably experiencing here is leak back at the pump. There should be a check ball or some means to prevent fuel from flowing back through the pump after it's shut off. This ensures fuel remains in the lines when the vehicle sits for longer periods of time (days). What you are describing seems to indicate the pump may be on its way out.
The other stuff you mention about amperage and the sort seems to jibe with my thinking of how things should operate normally. I don't think the issue lies with the fuel regulator. Only excess pressure should flow past the regulator, though.
Adding to help clarify a couple of points.
The idea of the vacuum on the FPR is to account for engine load. As you step on the pedal, vacuum goes down. As vacuum goes down, the FPR pressure goes up. This allows for more fuel to flow through the injectors at the same pulse width. I'd equate it to how the enrichment circuit on a carburetor works. The idea is to give the engine a little extra shot of fuel so it doesn't stumble as the fuel management is trying to catch up the needs of the engine. The vacuum response won't last very long, so the higher fuel pressure won't last very long.
As for your amperage going up, that's an easy thing. As fuel pressure goes up, the pump has to work harder. When you clamped off the line, the pump is fighting against the pressure harder, so the amperage draw becomes larger. If you had zero back pressure, the pump would be able to do its job much easier, meaning the amperage draw would go down.