So you want to know how much water a certain surface adsorbs. This is really dependent on the surface material/conditions. Check adsorption and relative humidity on Wikipedia. To where I have analyzed, it seems that there is about enough information in the two articles. I am not a specialist on the subject so I might be missing some important factor.
I will focus on just a little bit of one of your questions - the relationship between compressibility, density and pressure - and per my comment, recommend that you narrow down the scope of your question.
As you know, in a gas we experience "pressure" because molecules hit the walls of the containing vessel. When I double the number of molecules in the same volume at the same temperature, I double the number of collisions (each imparting on average the same momentum) and thus double the pressure - this is the familiar ideal gas law.
Now when the size of the molecules becomes a sizable fraction of the volume, the rate of collisions goes up. Imagine a pingpong ball between two walls. If the distance between the walls is large compared to the size of the ball, the time for a round trip is inversely proportional to the size of the ball; but as the distance approaches the size of the ball, the rate of collisions goes up rapidly.
I think a similar thing happens with "nearly incompressible" liquids: there is a small amount of space between the molecules, but they are permanently bumping into each other and into the walls of the vessel. As you increase the pressure, they bounce more frequently as they have less far to travel before they collide with another molecule (or the wall).
All this is still treating the liquid like a non-ideal gas. In reality, not only do you have the finite size of the molecules, but also attractive forces between them. Both these things make the picture a bit more complex than I sketched. But I would say that the above reasoning nonetheless applies (with caveats).
As for the experiment you described with stoppers on the inside or outside - there are other things going on there as you go from the static (no flow) to the dynamic (flow) situation - the water needs to accelerate before it will flow out at a certain velocity. But I think all that should be the subject of another question.
Best Answer
The mechanism is explained, e.g., in W. Johnson, Int. J. Impact Engng, Vol.21, Nos 1-2, pp. 15-24 and 25-34. 1998.
The following main assumptions are used to derive the approximate Birkhoff formula for the critical ricochet angle for a spherical projectile:
(i) The pressure $p$ on a spherical surface element along its outward drawn normal is $\rho u^2/2$; u is the forward speed of the sphere resolved along the normal.
(ii) The pressure applies only to those parts of the sphere which are immersed below the undisturbed surface of the water. The effect of the splash on the sphere is considered not to contribute any pressure.
Thus, I believe, surface tension is negligible.