Help understanding electron flow through coupling capacitor
Scenario 1: When the LM741 output voltage goes from a set value to a
  more positive value electrons flow into the LM741 energizing the
  capacitor as show in the image below:


This is not correct. The capacitor has already been 'energized' (charged up to half the supply voltage) by the op-amp's steady state output voltage. When a signal causes the op-amp output to go up or down the capacitor remains charged to half the supply voltage. It passes the signal through to the volume control by maintaining a fixed voltage between its terminals. Since the DC voltage at the pot is zero volts, at this point the signal will go above and below ground.  

The capacitor is only able to pass the AC signal through because it does not become energized and de-energized as the signal goes up and down. As the frequency is lowered however, the capacitor will indeed start to charge and discharge, reducing the output signal level. 

If you feed in a low frequency square wave you will see the output droop towards ground as the capacitor charges and discharges exponentially (with a time constant of 10uF * 10k&ohm;). The trace below is an example of what the input and output waveforms look like when a low frequency square wave is passed through a capacitor.