Part 2) Adding a resistor and a capacitor on the inputs and outputs of the circuit is good because it can block the DC power. This is because audio input should be AC and the battery itself is DC power.
The obvious difference between the non- inverting and inverting input waves is that between the two channel waves in the inverting, the waves are heading the opposite direction when they move unlike the non-inverting input where they move in the same direction.
Trouble shooting
When using the oscilloscope, the two black probes for both channels connect to the same ground cable.
Sean's Music Tech Blog 