Discontinuity
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To change density there are three ways. You can change the shape, mass or volume of the object
When mass increases and volume stays constant, the density increases. When volume increases and mass stays constant the density decreases. When they both change, then the density will depend on the rate of change of mass and the rate of change of volume.
Density does not change regardless of where the object is. It is a constant.
Density usually changes when an object is heated or cooled - especially in the case of gases, or when there is a change of phase.
It is unchanged. The density is the mass divided by the volume, and as both of these numbers are halved the density does not change.