How to identify that a given fan is a compressor fan or a turbine fan, just by visual inspection? Also, can visual inspection of a fan help in identifying the compressor/turbine stage i.e. if the fan is from a High Pressure Turbine/Compressor blade or Low Pressure Turbine/Compressor blade?
Assuming we are speaking of axial compressors/turbines
Compressor blades are generally thin and straight, and resemble a tiny rectangular wing with low camber thickness.
Turbine blades are more curved, often in almost "U" shapes (like the ones seen here). In particularly large and recent engines, where efficiency is critical, turbine blades will often be full of tiny holes:
To distinguish between high pressure and low pressure stages (compressor or turbine does not matter), the length of the blade and its torsion (i.e. how much the aerodynamic profile turns around the axis of the blade going from the root to the tip) are key: shorter and more twisted blades will be high pressure ones, longer and straighter blades will be low pressure.
Note that two blades of the same length could come one from a high pressure stage and the other from a low pressure one of a different engine: "short" and "long" are relative to the engine size.
On the other hand, radial compressors and radial turbines are more difficult to distinguish.