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Your pic doesn't indicate what part you're referring to. There should be a set screw in the handle base under the lever that holds the handel in place.
Well, that is an unusual setting :)
Often you have a "trap door" the other side of the wall. In this case it look like they made the trap over the ceramic so the whole big square would unscrew and this would let the vertical rectangle part alone hanging on the pipe. You then probably can see how to unscrew the robinetry with a wrench. That is my guess to that curious installation.
Ideally, the good way would be to not do it just like it is but make an access trap on the other side of the wall (i have not enough detail right now on that wall).
We also don't know if water got in there over time, you may have big surprise (rotted structure, mold...) that require lot of additional work.
"IF" everything is fine, it probably because the small vertical rectangle have a big enough overlap to provide enough surface to act like a flange that can make it water tight with enough caulk. You can also seat the robinetry on a thin silicon ring (that cured before, then you can screw the faucet to have a good pressure on it).
I don't know what the back panel material is for that frame. Again if no water got in it might be a water proof material that cover all the back of the frame. Meaning only the screw holes are to make sure no water will go past them. The area just at the bottom of the panel touching the bath will have to be checked also.