Why the water remains on the surface of the Earth? What makes the water stay on the surface? Why the earth does not absorb the water in it? 
 A: One has to study the geologic structure of the earth:


Figure 1: The interior structure of the Earth, with a close up of the lithosphere/asthenosphere boundary. Redrawn from Plummer & McGeary, 1997.

There exists the Oceanic crust, which is the boundary between the bulk of water and the lithosphere. It has very low permeability and thus the oceans contain the water like a bowl of ceramic. A crust exists also under the continents. There the aquifer can be fairly deep and hold a lot of water
The mantle is generally hot  and any water seeping  there would turn to steam and contribute to the gas pressures of the lava wherever it appears.
A: Gravity. As nearly as possible, the materials of the earth have migrated vertically so as to approach an arrangement closer to hydrostatic equilibrium.  Liquid water or water vapor is much less dense than rock, and can flow through connected porosity in the earth's crust.  In rock at depth, the weight of the overlying rock deforms the rock, collapses pores, and displaces water upwards towards the surface. Water can also dissolve as a solute in molten rock and can be a component of hydrous minerals, these materials are denser than liquid water and could carry water at much greater depths in the earth. However, because we find water at the surface, and because some water is outgassed by volcanos, we know that not all of earth's water is held in the interior.
Inclusions found in xenoliths and minerals can provide some evidence of what hydrous minerals exist in the earth's interior. The possible amounts of these minerals can only be constrained by geophysical measurements of the earth (seismic properties and density ect.) and what we can learn about the chemical and physical properties of these minerals through theoretical computation or laboratory experiments. For example:      
Compressibility and Thermal Expansion Study of Hydrous Fo100 Ringwoodite with 2.5 wt % H20 
A: I think the answer to this is actually pretty complicated, and has to do with chemical changes that take place in rocks during subduction. Rocks generally do like to absorb water (they become hydrated), but under the intense pressure and temperature of the subduction zone, the water molecules and the minerals become separated. I don't know exactly why this happens (I actually asked a couple of geochemists about it once, but I didn't know enough chemistry to understand the answer) but I think it's basically because dehydration is an endothermic reaction and a lot of heat is being supplied. Once this has happened the water is less dense than the rock and somehow makes its way back to the surface.
Having said that, the mantle probably isn't completely dry. I think it's very difficult to estimate how much water there is in the interior of the Earth, but some researchers think the moisture content is important for lubricating the movement of tectonic plates. But although they contain some moisture, rocks in the mantle are generally much drier than those on the surface. We know this because when new rock is exposed due to the spreading of tectonic plates, it undergoes hydration reactions that release a lot of heat.
So the the main forces that keep the water on the surface of the planet are to do with plate tectonics. If the plates were to stop moving, the water probably would eventually be absorbed into the interior, although this process would take a very long time indeed.
A: Its called specific weight and water has smaller specific weight than rock, if you find water between rocks that only because it is replacing the air in the fissures that would be there otherwise. It is the same question to ask why hot-air balloons fly. Same thing because hot-air has a smaller specific weight than cold air. 
A: In the last few weeks there was an announcement of huge amounts of water being discovered in the upper mantle and crust. It's hard to trust news articles written for common consumption, but it was calculated to be several times as much water as there is in the oceans, just under the United States (not even mentioning the other continents). After 4.5 billion years, it would not be surprising that the rocks below us contain a lot of water, as much as they can hold, and are probably in some rough equilibrium with the oceans and atmosphere.
I remember reading a few years ago that some geophysical models predicted that the rocks and oceans were not in equilibrium yet (and might not be before the Sun boils away the oceans). The concern was that the oceans would continue to be sucked into the crust and upper mantle (via plate subduction), eventually leaving the oceans dry. I don't know if this recent work lays that fear to rest, or what.
A: The Earth is 8000 miles in diameter. The average depth of the oceans is 12,100 feet. If you scale that down to a 40 foot diameter circle/ball representing Earth, the oceans would come out to be just over 3 millimeters deep on that 40 foot ball. That means that in proportion to Earth's massive size, the oceans are nothing more than a thin film of water covering its surface. Add in salinity, electromagnetism, electrostatics, surface tension, adhesion, cohesion, atmospheric pressure, subduction, surface irregularities, plant life, and the fact that there is no up or down in space, and you have more than enough natural phenomena to hold the oceans to earth.
