why is there a need for a centrifugal compresor, why bleed air isn't extracted from high pressure compressor stage in an engine - sure there is more than 32 psi of pressure? Than it will be cooled down and depressurised via expansion turbine?
The compressor drives the turbine. the two are connected and it is called an ACM (air cycle machine). Il the B787 this is electrically driven.
BTW are objects marked red on the picture below air vents for air to air heat exchangers?
Yes they are the ram air intakes for the heat exchangers. The air that goes in there passes through the heat exchangers and then goes overboard. It does not enter the cabin. In the cruise this is enough cooling for the bleed air and the ACMs are not really used at all.