No. Once your dropouts are adjusted for proper belt tension, they shouldn't need to be moved, ever. It's possible your belt might wear and stretch enough to need to readjust them down the road, but it should be well over 1000 miles before that's necessary. Once you remove the thru axle, your rear wheel can just drop out of the frame, the same as it would with any other drivetrain. When putting your wheel back in, take care to insure that your belt is properly engaged with the front cog first, and as the wheel is going in, make sure to align the belt in the rear cog and then finish installing your wheel in the frame and replacing the thru axle.
The Pinion Smart.Shift battery is tucked up inside the downtue of your frame. The charging port is a covered wire up near the head tube of the bicycle (it comes out of the frame with the shifting wire). The battery itself can only be accessed by removing the gearbox.
Unfortunately, it means you're stuck in whatever gear it died in. There is no option for changing the gear manually on the Smart.Shift gearbox. So make sure to keep your battery charged and ready for anything. On major bikepacking trips, we definitely recommend bringing the charger along with you.