The capacitance does not depend on the load or potential difference between the plates, ie it is an intrinsic property of the capacitor and if there is a dielectric medium between the plates, the electric field originated will be reduced in the region where the dielectric is present.
This happens because there will be loads of polarization in the dielectric, negative in the interface with the positive plate and in the interface with the negative plate.
There is a partial cancellation of the load on the board with the polarization load, which makes the surface charge density at the interface smaller. Boston Gear ORC1SANHP14P25
The capacitor has several functions, but one of the main is to store electrical energy. The energy stored in a capacitor can be calculated by the work required to charge it. The potential difference between the plates is V = q / C, where q is the charge on the plates.
Energy can be recovered when the capacitor is discharged, so it is stored in the capacitor or, more precisely, in the electric field between the plates. The capacitor can then store energy, to supply it to the circuit at times of peak consumption or when there is a power failure.