home audio: How much current flows through my speaker amplifier's output?
You have asked a lot of questions.  I'll try to get all of them.

Your power calculation is correct.  You will see about 1.77 Amps RMS current whey your amplifier is delivering its' rated power of 25 Watts into an 8 Ohm load.

1)  The reason your measured power is so much lower is that most of the time, the amplifier is delivering only a fraction of its' rated power.  In addition, your multimeter isn't responding fast enough to show the peaks.  An oscilloscope monitoring voltage across a series shunt resistor will give you a better idea of the peak current.

2)  Your speaker volume controls are most likely "L-Pads".  This is a wire-wound potentiometer with two resistive elements that change simultaneously.  They are configured to keep the impedance as seen by the input terminals (the amplifier) reasonably constant as the attenuation is changed.  Wikipedia has a good description.

3)  Speaker efficiency varies greatly.  Some speakers can deliver significant volume levels with tiny amounts of input power, some speakers require large amounts of input power to achieve even modest volume levels.  It all depends on the complete speaker design: drivers, cabinet, crossovers (if any).

It is not likely that there are hidden power amplifiers driving your speakers but is it possible.