The physics
A dielectric slab weakens the field inside it. Its molecules line up, and charges appear on its faces. With the plates' charge kept, E = E0/K.
gap filled: C = Kε0A/d slab t thick: C = ε0A/(d − t + t/K)
Battery on: V stays, so Q and U grow K times. Switch open: Q stays, so V and U fall K times.
A metal sheet has no field inside. The gap acts as if it were t shorter.
metal sheet: C = ε0A/(d − t)
A filling sparks through when its field passes its dielectric strength. With the gap filled, that field is V/d.