My question here is, why do we need point 2 to be on the saturated liquid line, i.e. why do we need a saturated liquid for the throttling process? Why can we not use it in the liquid region or subcooled region?
Similarly, why do we need a saturated vapor to enter the compressor (point 4)?
State 2 does not have to be on the saturation line. For the refrigerator to work it must be such that after throttling it ends up on the two-phase region. However, the more to the left state 3 is, the more liquid we have in the evaporator, which upon evaporation will produce more refrigeration. On the other hand, the further you push states 2 & 3 to the right, the more cooling you need, which could require a higher $P_\text{high}$. Placing state 2 on the saturation line is a reasonable compromise and a standard design convention.
As for state 4, it does not make sense to operate the evaporator past the saturated vapor. What causes refrigeration is the evaporation of the liquid at $T_\text{low}$, which draws large amounts of energy, while keeping temperature constant at $T_\text{low}$. Past the saturated vapor the temperature increases (the evaporator operates at constant pressure), which is to say that the freezer is getting warmer.
In practice, the point 4 must be beyond the saturation curve (more to the right), it is an overheating of the gas to avoid a cold blow to the piston of the compressor.
PS: It is necessary to limit the overheating because it acts on the perfermances.
