The scenes of the case "absorbing" the blood are clearly filmed in reverse. The "hidden" bladders oozing out the blood are clearly visible, and disappear in the later shots after the blood has supposedly been "absorbed". The blood being "absorbed" is just the blood being squeezed out, shot in reverse to give the appearance that the blood is being absorbed into the wood.
Geary is supposedly watching himself on TV as he's in the bath, but Pratt throws a radio into the tub that Geary's voice is coming from.