Why does inverting a song have no influence? I inverted the waveform of a given song and was wondering what will happen.
The result is that it sounds the exact same way as before.
I used Audacity and doublechecked if the wave-form really is inverted.
The second thing I tried was: 
I removed the right channel, duplicated the left one and set the duplicated layer as right channel. This way I made sure that both channels are exactly the same. Then I inverted the second channel only. I thought that this would create some kind of anti-noise, but it didn't.
Why is that?
 A: Re your last question: what you've achieved is essentially the same as if you wire one of your speakers the wrong way round so it moves in antiphase to the other speaker. In principle there will be points equidistant from both speakers where the sound waves cancel and you get a quiet spot. However as soon as you move closer to one speaker than the other you no longer get perfect calculation. Plus unless you're in an anechoic chamber you get sound reflections that mess up the cancellation. In practice it's very hard to get the sounds to cancel.
This principle is used in active noise control to reduce noise, but it does require very precise control of the sound phase and volume.
In the HiFi world connecting one speaker the wrong way round is something most of us have done at some time. It doesn't cancel the sound, but it does mess up the stereo imaging and make the whole thing sound rather muddy. This will be more pronounced the better the HiFi.
A: Inverting a waveform is the same as rotating your speaker around 180 degrees to face away from you. (Yaw or pitch - not roll!)
The changes in air pressure your ear detects is exactly the same.
A: The human ear responds only to the intensity $I$ of the sound it receives (more specifically, to the intensity distribution over the different frequencies) and this goes more or less like the square of the amplitude,
$$I\sim A^2.$$
Changing the sign of the waveform changes the sign of $A$, which has no effect on $I$.
