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Originally Posted by B.A.S.E 
1) Is that polarity or phase that has to do with whether the speaker membranes go up and down ?
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Short answer: Polarity.
Long answer: With a periodic wave you can also "invert the polarity" by shifting the phase by 180 degrees but you end up with a delayed signal. Depending on what you are doing, this might be an issue or not.
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2) I know it's mastering and not mixing, but is it wise to shift the phase of only one stereo channel ?
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No! Unless you are looking for some weird effect.
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I do that on my sinewave basslines and usually, I found it help getting with some mixing problems I have.
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This is a very bad idea! Maybe one of your speakers (or some other equipment in your system) is wired incorrectly?
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The only thing is that so-called "phase cancellation" when it goes mono.
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Not just in mono, if you stand on a line stretching right between the two speakers it will also cancel out. Don't do it!
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3) I don't quite understand the difference between polarity and phase invertions even with what I tried to grasp upon the internet...
If I take a sinusoidal function, inverting the polarity is equivalent to have the negative value...
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Not quite. See my other posts.
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Yet, if i take the same sinusoidal function and I flipped its phase, it means I add 180 degrees to it... thus, it should give me the negative value too, doesn't it ?...
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Yes but it is time delayed while flipping the polarity doesn't change the timing. And as pointed out before, you can't shift the phase of a complex wave.
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4) what about all digital tracks ? there shouldn't be any difference ?
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Not unless some piece of software/hardware is broken.
Si je peux te suggerer de relire mes messages precedants, les choses devraient se clarifier.
Alistair