He is under the water.
(source: ytimg.com)
He is below the water.
can be understood to use "water" as a layer which something is underneath
>The Abyssal Plain and Oceanic Crust is **below** the ocean
He is in the water.
has the meaning of being surrounded, in part or in whole by water. If you are under the water, you are also in the water. If part of you is above the water's surface, you are in the water.
Of your prepositons, one can only "Splash in the water".
on the water.
is usually used to describe a boat during an activity, since it is "on the surface of the water"
The boats are sailing on the water.
whereas
in the water
is usually used to describe a static position of a boat
>We took the boat from dry dock and put it **in** the water.
We launched the boat **into** the water.
