Answer to "Why playing via AUX cut's on quiet passages in the songs/movies?"It is possible to hack the pcb to fix it. Extract the board, locate Q12, and solder a wire that shorts its collector (middle terminal) to ground. This will make Flip 4 think there is always audio going into aux. You may also want to remove 33-ohm resistors, that may reduce distortion for signal sources that have high-ish output impedance. This hack causes a few side effects though: Bluetooth pairing sounds will not be played. Bluetooth audio does work, just no pairing sounds.
Answer to "Why playing via AUX cut's on quiet passages in the songs/movies?"As a workaround, you can run a signal generator app in the background, set to very low frequency like 20 Hz, and low but not too low amplitude. Flip4 will reject this frequency and not distort/waste power, but it will be alive all the time.