Is placing drawings and pictures—drawn on paper—under the bed or mattress considered a degradation of them, or is it a condition that they be on the mattress itself to be considered a degradation, knowing that they are incomplete in creation?

There is no harm in drawing, making, and possessing images of animate beings that are incomplete in their creation (such as images without a head or torso). As for images that are complete in their creation, it is forbidden to draw or make them, and it is forbidden to possess them if they are hung or erected for veneration. However, there is no harm in placing them on the ground or under the bed, as this constitutes degradation.