Can we save the light energy as it is ?

Humanity has already 'saved' light energy, however it is mostly in the process of the absorption of light energy and converting it into electrical (think solar cells). These processes are very inefficient as the most advanced solar cells can only store/convert about 15% of the energy within the light.

To truly save light energy as it is however involves using materials that absorb the light's energy very minimally and also allows the light energy to sustain it's energy wave. Something that humanity cannot perform at the present.

Those little glow in the dark plastic things that store light are the only thing I am aware of that comes close to answering your question. obviously they are not very efficient and I'm not sure what the chemical process is and don't know how you could save it for when you need it. To date the most efficient way to do this is to use solar cells to convert light to electricity and then store the electricity in a storage battery until you need to convert it back to light.

There's no theoretical reason, just practical ones. A resonant circuit of an inductor and capacitor store electromagnetic energy by having it convert between the magnetic field of the inductor to the electric field of the capacitor. A gas laser can have nearly perfect mirrors on each end, and light does make many trips through the laser. But in all these cases, the energy density is not very high, and the losses dissipate the wave in at most seconds.

Not directly or very efficiently indirectly ; for example, the energy could be converted to electricity via a solar cell then stored in a battery chemically.

No. It involves entrapping a traveling wave.