A capacitor is much like a water storage tank. A conductor is something a pipe.
Electrons flow in a conductor. Water flows in pipe. Not exactly the same.
Just like a pipe can fill a storage tank it can also empty the tank.
I do not know which you are talking about.
A inductor is more like a long long pipe. A pipe so long it take time to get water into it and out the other end. When the pipe is flowing it stores water. (not a great example but a start)
Many bigtime semiconductor manufacturers that deal in SMPS components have design sheets and application notes for these exact questions. I would start there for help regarding the devices you're using — if you're currently using any.
The water analogy for circuit components is a really good way to intuitively understand electric circuits. The water flow = electric current and water pressure = electric voltage.
A capacitor can be imagined as a membrane that is fixed in a tube. If water is flowing in the tube the membrane will be stretched and the water pressure in the tube will be increased.
An inductor can be imagined as a flywheel which is mechanically connected to a paddle wheel that is moved by the water flow in the tube. In order to rotate the flywheel some water pressure is necessary.
With this analogy it is easy to understand e.g. a resonant circuit (see attached file)
Actually the underlying differential equations to describe either this water circuit or electric circuit are structurally the same.
Not sure if the question is more about the underlying physics and not an analogy. Energy in a capacitor is stored in an electric field which is only existing if there is a voltage on the capacitor, energy in an inductor is stored in a magnetic field and only present if a current flows through the inductor.
All that stuff is finally represented in Maxwells equations.