Where to start???
"** Sec. Air System Monitor INCOMPLETE ** (what is it?) "
Yes, I think I can answer that question. The whole list you have given are called monitor tests. They represent specific testing required to maintain OBDII standards. The testing can be done in various ways by various manufacturers and is sometimes not required or inactive. These tests can be intrusive at times and are generally done (quickly) when the conditions are correct.
In the case of secondary air. This is the AIR pump. Air thats is directed to the exhaust during cold running to continue the oxidation process and heat the cat. The monitor test which only is conducted under certain conditions, excites the pump and looks for an immediate reduction of O2 sensor voltage below 100mv (I think). The test as run by the scanner powers the pump after closed loop and asks for the above voltage after some real long time like 20 seconds. In reality the voltage drop is almost instantaneous if the pump is working. BTW any Air leaked through this system after closed loop would probably cause a P1132 code among others.
The sec air system has an off/on control valve after the pump, before the exhaust. It must be closed after cold running to prevent air from being aspirated through the pump into the exhaust.
Got to go but for the rest I must say that many manufacturers and OBDII regs state adaptation values different; block learn, integrator values, percentages, etc. I do not recognize the numbers your scanner gives. The 271 doesn't ring any bells.
Bosch Master, ASE Master, L1
33 years MB technician