The arduino A/D sampling the signal in 10-bits of information but the output should be in terms of 8-bits. Moreover, the chip produces noise also when there's no signal at all, therefore values below the noise level should be nullified. These code lines make sure the 10-bit value will be over the noise level and mapped into an 8-bit value. The code was working as it should and now I was ready to continue to the integration.
Pin8 controls the clock oscillator which produce the band-pass filters, therefore it should have on its input the precise values of 200KOhm resistor and 33pF capacitor.
Two more capacitors are connected between VCC and GND and from pin 6 to GND.
The "audio in" plug usually has at least 3 pins: Left, Right and Ground. It is enough to connect only the ground and one of the channels.
Pin 5 should get the audio signal. The MSGEQ7 amplifies the signal in 20dB (x100), so a good value of AC voltage at the entrance would be around 30-50mV, then the highest output values will be 3-5V. The potentiometer and a resistor connected to ground are exactly for that reason - Then you are not depended on the external music player volume. The 10nF capacitor should filter the DC offset. EDIT: Later, I found out a 68nF would do a better job.
On the arduino: Pin2 - Strobe, Pin3 - Reset, Pin4 - Led Strip, A0 - Analog in.