Now that I have more time to respond...
Your question mentions RAT. The only place I've ever seen RAT used is in the DC8 and DC9. Where are you seeing RAT?
SAT is STATIC air temperature or the actual air temperature before the fast-moving airplane came along and disturbed it. i.e. when the air was "static".
TAT is TOTAL air temperature and is SAT plus ram-rise. Ram-rise is the increase in temperature due to the fast-moving airplane coming along and disturbing the air. The air heats up due to the friction of the airplane's movement through it.
Before fast airplanes had air-data computers, to do all the math for us, we had a temperature gauge which read something between SAT and TAT. It "captured" most of the ram-rise but not all of it. The RAT in the DC8s and DC9s that I flew was such a temperature probe. There was no display of TAT or SAT in those airplanes but that was okay because all of the performance charts used RAT on their temperature scale for airborne calculations.
The engineers would know the ram coefficient (Ct) for the RAT gauge--typically between .8 and 1.0). If the Ct was 0.8 then the temp gauge was displaying SAT plus 80% of the ram-rise. This Ct could be used to more accurately calculate performance values, such as true airspeed, based on your indicated temperature on the RAT. In practice, we never used Ct, we just used performance charts that had it built in.
As far as the pressure altitude, all methods of calculating true airspeed that I'm aware of use pressure altitude. It makes no difference at what altitude you are flying because pressure altitude is pressure altitude at any altitude. Just set your altimeter to 29.92, if it isn't already there, and read P.A. for use in the calculation.
Compressability comes into play at higher speeds because, at those speeds, the air can't get out of the way of the airplane fast enough and is compressed somewhat creating a higher localized air pressure. This adds an additional error in your indicated airspeed that must be corrected in order to calculate true airspeed. IAS is corrected for installation error to get calibrated airspeed. CAS is corrected for non-standard pressure and temperature and compressability to get true airspeed. At the slower speeds typical of G.A. airplanes the compressability errors are small enough to be disregarded.
The CR-style flight computer (Jepps CR-2, CR-3, and CR-5) had provisions for calculating true airspeed, corrected for compressability, and also returned Mach and ram-rise. Here's a picture.
http://www.stefanv.com/aviation/flight_computers/cr.jpg