I'd rather just say that the horizon and mass of the hole shrinks, than say that the hole is "filled in".
It's not possible to define the mass of the singularity, but the black hole itself has a mass. And yes, a singularity is a "hole" in general relativity; GR fails to make predictions about singularities.
It has mass-energy, like any radiation. If you enclosed some of it in a box, the box would have mass.