Another possible factor (especially for 3) is that the tripod mount socket on the camera isn't centered perfectly on the nodal point of the camera, so your rotation isn't just a rotation, it's a rotation and a shift.
The tripod socket is properly centered, as is the socket on the bottom of the camera.
However, I think I have a clue as to what happened. See the two attached photos, the first with the tripod facing due West, the second after panning the tripod around so it faced due East. To take these photos I had the tripod on a perfectly level tile floor, and the level indicator built into the tripod said it was straight. I confirmed that the center post of the tripod was vertical with another level.
tanstaafl.
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