Have the backgroundpattern made of alternating pieces of absorbent and transparent material, then. (I assume the machines work by measuring obstruction of rays. If they work by reflection of rays, then replace "absorbent and transparent" with "absorbent and reflective".)
Yes, that is basically what I suggested, the material (film) would just drape over the backscatter plate. The resultant image (without a subject) would resemble a black / not so black checkerboard pattern.
The image appears to be a negative relative to the amount of xrays reflected back to the xray source so the additional material would simply have to be slightly less reflective (more absorbent) than the backscatter plate.
No, the image is the positive of the reflected xray, white is more backscatter. Metal has little backscatter and neither does empty space. There is no 'backscatter plate' in terms of a background required to generate the silhouette as far as I am aware.