Let's say it's the start of the day. One does a full IMU calibration. When you change batteries, do you need to run another full IMU calibration? Or does the calibration hold over through the shut down/battery change?

The calibration should hold. If you want to verify it do a calibration jot down the figures and remove the battery wait a while, insert the battery and recheck your settings. They should be the same.

Wow, i've done one IMU calibration when I first did firmware update and that's it.  Should only be calibrating the IMU if you are seeing drift or the numbers are out of tolerance.