Mutual inductance vs coupling coefficient
Experimentaly, how should I measure coupling coefficient and mutual
  inductance between these two planar coils?


You start by recognizing that with no load, and perfect coupling (100%), the output voltage from coil 2 is slightly less than the input voltage to coil 1. This is because the two inductances are not the same (24uH to 20uH) and this results in a turns ratio of 1.0954:1.

In other words the square root of the inductance ratio is the voltage coupling ratio (turns ratio) when the two coils are perfectly coupled. So, with 1 volt p-p on coil 1, coil 2 produces 0.9129 volts p-p into an open circuit load.

When the two coils are not perfectly coupled (say 50% coupling), coil 2 only receives 50% of the flux generated by coil 1 hence, the output voltage will be half of 0.9129 volts i.e. 0.4564 volts p-p.

So, you can use the voltage level on coil 2 for predicting the coupling factor but, be aware of parasitic capacitance - if you are anywhere close to the natural resonant frequency of either coil you will get voltage magnification effects that ruin the ability to predict the coupling factor.

Try and use the lowest frequency you can for this experiment and stay way-below resonances.