FBW,
It depends what airplane you're looking at to determine whether IAS or CAS is displayed to the pilots. If the airplane has a 'compensator' built in to take the readings from the pitot probe and correct them, then you will get CAS in the cockpit. A lot of airplanes don't have this function so IAS is displayed and there is a chart in the AFM where you can see what the CAS is for any particular IAS within the speed envelope.
As for stall speed changing with altitude - yes it does. Usually very small changes though. The 'truest' indication of performance deficit or surplus is measured based on EAS - even though your stall speed will be published in IAS, it is the EAS that matters. When you climb the air becomes more easily compressible and, therefore, there will be a bigger difference between IAS and EAS at altitude versus SL. The IAS stall speed will increase with increase in altitude so as to keep the EAS the same. That takes care of the compressibility problem. There is also the effect of Reynolds number. There are other people on here better qualified to talk about the effect of Reynolds number on the aerodynamic forces created by an airplane but the general principle is that Reynolds number decreases with increases in altitude and decreases with decreases in speed. You can find out more about it here:
Reynolds Number
All in all, the changes are
very small mostly because the stall speed is a relatively small number (the smallest in the normal flight envelope). If an airplane stalls at 120 KEAS at SL, it stalls at 120 KCAS. If it's at 35,000' the KCAS becomes 121.6 KCAS - a difference of only 1.6 knots!