How to identify which transistor is in active region and which one is in saturation?
2 different equations for drain current, one for active region one for saturation.


You're mixing FET and Bipolar vocabulary, which is confusing. Bipolars have Saturation and Active region (and quasi-saturation in-between). Saturation occurs at low Vce, when the B-E diode passes high Ib.

For FETs the terms are the opposite:


"Saturation region" is the mode you use to build an amplifier, as is the case here. The term "active region" is much clearer, so that's what I'd use. The FET behaves as a voltage-controlled current source which is characterized by Id as a function of Vgs (and Vds), and transconductance is d(Id)/d(Vgs).
"Triode mode or linear region (also known as the ohmic mode)" occurs when the FET behaves like a resistor (hence "ohmic mode" is the most explicit).


If you want to build a common source amplifier (which is the case here) you need transconductance, which means using the active mode. Thus, do the calculatoins assuming active mode, then check that the FETs are indeed in active mode (saturation).