Do the rocks below an active sill go down, or those above go up, or both?
It's both. The rocks above the sill go up, whereas those below it go down. For shallow diking events it's mostly up.

This is all based on theory of linear elasticity. People model deformation using elasticity all the time, especially for studying deformation at volcanoes which one can measure using GPS, leveling, InSAR, etc.