Hysteresis allows the computer to use one set of readings on the way up, and another on the way down i think. Basically if you are fluctuating right around your fan turn on temp they will cycle on, off, on, ect. A larger hysteresis keeps it from doing that i think.
For PE don't you have a pe multiplier? Even if you have the afr tables that is not perfect. The computer may think it is comanding a 12.5:1 afr, but you may really have 14:1. Reasons for this would be differences in actual airflow vs. reported airflow via ve and maf tables.
Reasons for changing the maf would be for the above. Maf's aren't perfect by any means, and if you think the maf is off it may need to be re-scaled. I know when i put a full size truck maf on mine i put the full size truck maf table in my truck. But it ran like garbage, way lean, i had to bump the table up considerably. Many factors can play here, intake shape and geometry, maf sensor variations, engine characteristics, ect.
You should be open loop(not using o2 sensors) at wot, because the computer is commanding non stoich mixtures, and it can't measure those with the stock narrow bands.
Iac valves are stepper motors. You energize a set of coils in the motor, and the motor turns, and then it will hold to that step. If you have ever had a magnet on a table, and brought another magnet close, the one on the table will turn then hold. The computer extends and retracts the iac by timing what coils get power you can extend or retract the motor.
For your purposes big numbers are open, and small numbers are closed iac step wise.
There are some diagrams and such here:
MegaSquirt-II Idle Air Control