"...understanding is that it's purpose is to supply power, some way or another, to operate the injectors, thus not having that cyclical current running through wires near the radio..."

I believe that's exactly right. The ecu effectively grounds the injectors, but the ground path is back to the block.

"...somehow supplies power to the ignition system, and without this power, the fuel pump will not operate..."

No and yes.

The relay does NOT control the power to the ignition system. However, the FI ecu senses the ignition PRIMARY (that's the 12 volt stuff) and detects pulses. If no pulses, then the fuel pump relay drops out after ~1 second.

"...if your car won't start, but you can hear the pump running, then the RSR must be OK..."

Not necessarily. The fuel pump current is not controlled by the radio suppression relay -- it switches power to the four injectors ONLY. If you hear the pump running it means the fuel pump relay's OK and that the ecu detects pulses at the ignition primary. If, for example, the coil wire were shorted to ground you'd have no spark to the plugs but the injection system would be dutifully flooding the cylinders.....

Your pump could run fine but the suppression relay could simply shut off the injectors, starving the engine. Happened to wife's car two weeks after resoldering the fuel pump relay....

"...Regina system, do all injectors function simultaneously?"

They do on my '91 740 with Rex Regina.

Sleep tight!