I am not certain of the correct answers. Normally when modelling a combustion gas turbine for different ambient temperatures , I would assume:
for each site elevation , constant compressor inlet P and constant turbine outlet P
constant RPM and blade geometry ( duh)
constant turbine inlet temperature ( TiT)- but this can be calculated different ways depending on the means of cooling the combustor
constant volumetric flow entering the compressor- but this simplification assumes any bypass piping and throttling dampers are in a fixed optimum positions- this may be one reason that the isentropic and polytropic efficiency is varying in your performance review- modern CTG's fiddle with these vanes, dampers and bypasses to minimize NOx and maximize TiT.
If the turbine has a known and fxed "flow factor" for the gases entering the first row of blades, and it runs at a fixed TiT, then the combustor pressure must vary with gas flowrate. Its not clear if this implies a constant pressure ratio across the compressor for various ambient temperatures.
But I am sure there are books and papers that will rpvide simple thermodynamic models to explain the issues you found.