Distance to the hole Just so I am understanding you correctly, for the entry on any hole should it be (1) the distance of the hole or (2) the distance I have left after my tee shot?

The “Distance” entered is always the distance of the ball to the hole at the beginning of the shot. For example, the tee shot of a 440-yard hole ends up in the rough 165 yards from the hole. So you’d enter 440 for shot 1 and 165 for shot 2.
You should always enter the distance to the hole and never the shot distance. This always, or almost always, makes data entry much easier (not sure how shotscope presents the data).