You post things like this to gloat over the rest of us poor folks stuck looking at cube walls all day, don't you?

The answers to your questions are basically what Bitt said -- lens curvature. Some stitching software will correct for that before stitching. 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 way stitching software gets around something like the discoloration mentioned in X is to blend images where they overlap, rather than just abutting them at the edges, or doing a simple overlay.