monitor test run frequency, are they the source of error codes?

What is your question?

The OBD II system on my vehicle has 8 monitor tests of which 5 immediately run and complete then the O2 sensor runs and completes with in a couple of starts leaving the CAT and EVAP tests to run and complete. The CAT test has been taking 46 to 53 starts to run and complete and seems to run in local traffic conditions with starts and stops with the engine idling when stopped at intersections. Once the CAT completed it generated a P0420 and P0420 Pd. I did not clear the codes then with in 23 starts after the CAT test had completed the EVAP test had completed. It seems to like to run when the temperate is between 50 and 75 degrees F. It had been in the mid 80s prior to a recent cool spell in my area and the EVAP test would not run and complete no matter how or how many times I drove the car. So now then I have all eight monitors run and completed and P0420 and P0420 Pd error codes and a check engine light on. Questions: I assume my PCM continually runs these tests in some frequency and once a given test completes if there are problems error codes generate then the PCM moves on to the next test and repeats the process until all the tests are run and completed? I assume the only way an error code could be created or cleared is by a monitor running and finding problems generating error codes or running and not finding any problems no error codes are generated and if there are existing error codes the monitor will clear them once the test has completed? I assume the CAT monitor test has multiple sub tests that it generates given the number of starts it takes to complete and the only way to see them is with a scanner that cost several hundred dollars? If my above assumption is true and I looked at this information and saw the error codes are the result of something happing in 2 out of 53 times there might be a change the tests would run and complete with no error codes otherwise I could only assume the problem would have to be fixed before I could expect to see all completed test with no error codes? I assume my OBD II system will generate a P0420 if my catalytic converter efficiency drops below 95%? In looking at replacement catalytic converters I have found the EPA places a lot of standards on people that make and install aftermarket converters. They require a 25,000 compliance warranty and 5 year 50,000 mile warranty on the metal outer housing and there don't seem to be any standards on OEM products and in many cases OEM converters are re manufactured with only 1 year 12,000 mile warranty so I really don't know if I would get better at the dealer or not? Any insight or feedback would be appreciated.