1- What we call this opamp configuration?
2- What's the advantage and the disadvantage of this circuit?
3- And what's the purpose of the L2 in the feedback?

I have changed gradually the value of L2 from 1 pH to hundreds of H but nothing noticeable, then I replaced it with a resistor and did the same process the result was the same, in the end I replaced them with a wire the result was also the same.

Edit: this circuit was designed in National Aviation University of Kyiv, Ukraine.

The circuit is suposed to exhibits a maximum in-band total harmonic distortion (THD) of 1.7%. And a maximum in-band phase noise of −139.3 dBc/Hz at 100 kHz offset frequency and has an outstanding value of a standard figure of merit (FoM) of −198.6 dBc/Hz.

Edit2:
For question 3 the inductor L1 provides positive shunt–shunt feedback.

Edit3:

For question 1 the opamp configuration is a Negative inductance circuit, a type of negative impedance converter.

Negative impedance converter

This circuit can be configurated in different ways the negative of any impedance can be produced, including negative capacitance and negative inductance.