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>>"1. Why does AC mains polarity affect sound of an audio gear?"<<
It is very important, it can effect the sonics of a piece of equipment. If the AC polarity is reversed it also can cause hum when connected to other equipment by ics.
For a typical AC grounded electrical system you have a high side and a low side. The low side is the neutral. The neutral has a reference potential, voltage, to ground of 0 volts nominal. The high side is the so called hot conductor. The hot conductor has a difference of potential of 120 volts nominal to ground, (USA).
The power transformer of a piece of audio equipment has a primany and secondary/s winding. If the manufacture did his job correctly the low side of the primary winding will match the low side of the of the secondary winding and the DC power supply.
If you check the archives of Agon "Sean" goes into great detail how you can check each piece of equipment of your system for proper AC polarity.
If you go to the archives of "AA", "Bob Crump" went into great detail describing why proper input AC polarity is so important.
Chris I forgot to give you Bob Crump's (now deseased) Audio Asylum user name, it is "rcrump".