Let's jump directly into the setup
I took all the suggestions into account and I added a total of 5K gate series resistance and 1M pull-down resistor.
I also reduced the wires length and they are not overlapping any more.
It's worth mentioning that the more gate series resistance I add, the greater the voltage needed from the SG to open the gate of the MOSFET.
Let's see the wave forms:
The ringing is still there. I stand by my opinion that 15FR250E resistors are not suitable for measuring small currents at frequencies greater than 1KHz. In a few days I'll have another model to investigate.