As far as 4A staying on…and so forth between mode changes and power cycles. That is well documented.
If you are say in Sport, and turn the Truck off. If you start it back up an hour later, you will be in Normal, but with 4A engaged.
If you are in Sport, and turn it back Normal before you turn the Truck off, it will go back to 2H. You will be in Normal when you start back up.
If you do the first scenario, and want to get back to Normal without 4A, you do not need to change back to the mode you were in before, and switch back, just merely hit the 2H button. The mode has already been reset to Normal by the new start up, you just need to return to 2H.