During the SAT, do we compare the uncorrected temperature indication of controller with true test temperature (uncorrected test recorder reading + test thermocouple correction factor + test recorder correction factor)?
This is the standard method – using an uncorrected process control temperature.
AMS 2750D Example 2 seems a little bit confusing because offset and correction factor of furnace thermocouple are applied algebraically to uncorrected temperature indication of the controller although offset is already applied intentionally to the controller. If offset is an internal adjustment (already reflected in the displayed temperature), why we are applying it twice?
You are not applying it twice. The t/c correction factor involved in this calculation is the SAT thermocouple.
Pyrometry Reference Guide FAQ Question 42 states that applying furnace-sensor correction factor during evaluation of SAT is not correct. This means that there is an error in Example 2 in AMS 2750. In this case, we should never take correction factors of furnace sensors into account during SAT or TUS when evaluating furnace sensors readings. Is this correct?
Based on AMS 2750D, yes, it is true you do not apply correction factor to process thermocouple controller.
During the TUS, we collect data from furnace sensors and test thermocouples from test recorder. Since the test recorder takes the raw data (uncorrected) from all sensors, do we have to apply offsets and the correction factors of furnace thermocouples? For example, if the test recorder indicates the uncorrected reading of the furnace sensor as 996°F, and let the test recorder correction factor at this temperature be 0°F, then should I consider this value as 996°F or 996+4°F (offset) = 1000°F during evaluation of TUS?
Typically, the test sensor is left uncorrected, although if one were to have correction factors for temperatures, which are representative of the full range of TUS, then it could be argued you should apply known correction factors for the process thermocouple since you are doing so for the TUS thermocouples. Once again, I would verify this with the PRI staff engineer