Can a refrigeration cycle with fluid refrigerants work at variable evaporator and condenser temperatures without phase change?

Answer 1

Technically, yes. In practice, no. The latent heat (the energy required for a phase change to occur) is massive compared to the energy required to change temperature of a single phase substance. As such, you are only comparing:

mCp(T2-T1) of the two substances, where m is mass, Cp is heat capacity, and T is temperature. Even substances with high heat capacities like water will not cause a large temperature change in the the fluid you are heating up (or cooling off).

In short, while it would refrigerate, you would either need LARGE amounts of refrigerant (LARGE = the volume of a small creek) or a refrigerant so cold it might be in the solid phase. Otherwise, your temperature drop would be insufficient.

The other benefit of a phase change is a consistent temperature.