The audison balanced input is an interesting one, and I'm pleased to hear it works. If you're going to spend that much money, I always used Zapco and Symbilink, though, but good to know
We have other instances of amps working OK with balanced signals even though they lack true balanced inputs (such as LRx). DLS amps come to mind. The PDX amps are probably another case. These amps waste half the signal - the (-) is shunted to ground through a resistor capacitor network - but they seem to work. I don't like to recommend any amp I haven't tested in this manner in a BMW, though (I tested DLS amps on the TSX signal years ago).
There is not really any such thing as "noise cancellation function". I think what you are experiencing in #3 is that using a SPEAKER input for BALANCED signals doesn't work too well, because you are attenuating the signal - lowering its amplitude - and it's already low enough, so you make it too low and usually knock it into the noise floor. This is why I've been recommending against using Audio Control products with speaker-level inputs on balanced signals - un-needed attenuation.
But congratulations! Since you've progressed from Googling to actual testing, you have graduated from getting advice we can reasonably expect others to follow (which is never the full body of our experience) to going one step further and actually trying the installation and sharing your experiences!
No more explanations needed for you! Start that installation!