How do we check the load on a particular element cause by wave and current loading in Caesar (i.e. horizontal force cause by drag and inertia; vertical force cause by lift)

That loading is computed internally and used to build the "global load vector". These loads are not saved or output.

I need help with building the static cases in order to obtain pure wave stress. Please advice.

How do I get pure wave stress , what combination in loads?

Set up a load case with just "WAV1" in it.

Actually I need to get the forces and moment for pure wave case, because I need to combine with wind loads (generated as W+P1+D+T2+WIN1) and I don't want to overlap the operating.
The system which I am analysing is coming from the subsea section going up onto a marine platform. So wave will be active up to the splash zone (about 3880mm above the MSL, and after that wind will take over).
Thank you very much for your time in advance.
PS:Does Caesar calculate (after I input the free surface elevation, water depth and wave heigth) the LAT and HAT, how it works...I am doing this Wave analysis the first time...

Then why not setup your load case as: W+P1+D+T2+WIN1+WAV1 ?

You have to define which elements get wave load and which elements get wind load - you can't have both on the same element.

Please define LAT and HAT?

LAT = Low Astronimical Tide and HAT = High Astronomical Tide
When I input the wave load table, I fill in Free surface Elevation and water depth (are they always the same numbers?)Is Caesar calculating (in connection with global coordinates)the mean sea level?

"Water Depth" is the depth of the water at your location. If you need to consider tidal changes, then you can use WAV1, WAV2, etc where you vary the depth.

"Free Surface Elevation" does work in connection with the global coordinates you set in the piping input. For tidal considerations, it would be best if the first node of the model was at the top, with the model coded down to the bottom. Then the free surface would always be zero and all you would have to do is change the water depth. If the first node is at the bottom, and the model was coded upward, then you would need to adjust the free surface to consider the "other" tidal condition.