So this one is kind of easy but I can't find an answer anywhere:
When the anchor point is moved without using alt + drag, the position is supposed to change as an additive inverse pattern (so it adds when you subtract to each of the x and y coordinates) -- in order to preserve the position of the image in the comp (at least according to my book After Effects Apprentice). What mine is doing however is to move the same as the anchor point and the position is preserved.
Behind the scenes, how do the anchor point and position coordinates interact to draw the layer? What's going on here?
The anchor point is the center of rotation and the origin of scale. By default it is at the center of a layer.
The position is the position in the composition world space of the anchor point. If you use the pan behind tool or anchor point tool to move the anchor point around then the position will not change but if you change the values of the anchor point then the layer will appear to move in the composition window because the anchor point position is changing. If yo hold down the ALT/OPTION key while dragging the anchor point around with the Pan Behind tool you get the same results as scrubbing the anchor point values in the timeline. It should only take you a little while to get the hang of it. The most common use in my projects for moving the anchor point is to create hinges. I move the anchor point to where I want the edge of the hinge to be. Simple as that.