Quality Factor and Frequency Bandwidth in a matching network
1) I have always been told that the quality factor is the reciprocal
  of the fractional bandwidth (calculated by using as reference an
  attenuation of 3dB with respect to the peak of the
  impedance/admittance of the circuit considered).


Good for series RLC to parallel RLC, because we calculate Q @ resonance.


  2) We insert a parallel capacitance and then a series inductance. The
  second one is used to balance the reactive part introduced by the
  capacitance.


These matching networks are often designed for low Q. Q > 1 is always required when an impedance-matching solution is needed. However, the frequency response is not symmetrical above and below the frequency where impedance is matched....frequency response takes on a high-pass or low-pass form. Q is ill-defined here, especially where Q is low.
But the matching point, where all reactances cancel is very well-defined.


  3) The quality factor is function of frequency. Therefore, it seems to
  me that a certain transformation from series model to parallel one (or
  vice versa) is true only for a certain frequency.


At resonance the transformation using Q applies: RLC (parallel) &lt;> RLC(series).
For the "L" network matching RLC, resonance and Q are ill-defined.