Could compressor stalls be caused by air in supercritical conditions?
The answer to your question:


  Is it possible that supercriticality of the fluid (air) is one of the causes for compressor stalls or compressor surge ?


...is definitely no.

Stall is caused by an excessive angle of attack of the incoming air, relative to the blade. It can happen on the first stage (first row of rotating blades), where the pressure is no where near high enough to be supercritical. Surge occurs when the stall is very severe, so it’s the same phenomenon, just worse.

While the likelihood of a stall occurring is determined by measuring the total pressure distortion across the compressor face, it is the angle of attack that is the critical factor. Regions of low total pressure indicate the flow is likely to be turbulent in these regions, and therefore the angle of attack is not steady, and can exceed the ability of the air to follow the surface of the blade. Once it separates, it becomes turbulent, which means the blade does not perform its function of compressing it well. This is a big problem, as the compressor is trying to get the air to flow “uphill”. Stall generally starts as a phenomenon involving a few blades on one or more stages. It can then develop and cover a large section of the compressor. If the axial velocity of the flow through the compressor starts to vary, faster and slower, then faster again, it is called surge. The engine “chugs”.