What is the recommended fully-charged voltage for NiMH AA batteries?
I have done research on different batteries and cannot find a maximum
  OR minimum voltage to keep NiMH AA batteries within.


Well the very first hit when googling "NiMH AA battery data sheet" gave me this information: -



If different batteries are specified at different levels then there is no generic upper and lower limit.


  What do most electronics want and expect from the AA batteries they
  run on?


Most people regard the voltage output as being 1.2 volts nominally.