Something tells me this is a slightly bigger project than you think... And, you might not get the audio quality you are looking for without adding external ADCs & DACs...
Does this means that if I adjust the DC offset to 127, when the analog output value is lower to 127, the speaker receives an negative voltage?
If it is true could you tell me how to change this parameter?
I haven't studied that project and I'm not sure what they are trying to say...
But, the Arduino analog-to-digital converter reads from 0-1023. So with the internal reference set to 5V, you will read ~511 (not 127) with 2.5V applied. With silence (and the 2.5V offset), you will read ~511. If you apply an AC audio signal, your A/D reading will be less than 511 when the signal swings negative, and greater than 511 when the signal swings positive.
By subtracting 511 in software (in your sketch), you can take-out the offset.
Secondly, about the microphone and the amplifier, do know where could I find a tutorial or an example of program which could be applied to use for the amplifier?
Are you going to build an amplifier, or buy an amplifier?
You need a preamplifier to boost a microphone-level signal to (approximately) line-level for the Arduino (or for a hi-fi amp, etc.). If you want to build an amplifier, [u]National Semiconductor[/u] makes lots of audio chips and they have "application notes" with suggested schematics.
If you want to buy something, a [u]small mixer[/u] is usually cheaper than a separate preamp. (Make sure to get a mixer with a microphone input).
Finally, I have to idea how to define what kind of hardware (resistor's value, capcitor's value) has to be connected between analog ouput and my speaker to be compatible with the speaker's caracteristics (3ohms,55Watts)
You cannot drive a speaker directly from the Arduino. You need a power amplifier to drive a speaker. The wattage rating on the speaker is it's maximum rating, and you may not need 55W.
Again, if you want to build a power amp, National Semiconductor is a good starting-point. Or, you can buy a [u]small power amplifier[/u].