All of my textbooks mention, that entropy-change of all spontaneous physical, and chemical processes is positive, and that such processes need another condition to fulfill- decrease in the net internal-energy of the system, taking part in the process.
I just want to know that what is the reason behind this tendency of a system to increase its entropy, and to lose its internal-energy.
Perhaps my ensuing answer will be a little too simple to be satisfying to you, but I only have a firm grasp of things when I keep it simple.
Let's just consider statistical mechanics and look at the Canonical Ensemble (where there's a constant number of particles [N], volume [V], and temperature [T]). The components that make up this system want to reach equilibrium because that's how thermodynamic systems behave. The equilibrium point in the Canonical Ensemble is defined as the point at which the Helmholtz Free Energy, A, is minimized, and it's defined as: A = U - TS where U is potential energy (a negative value) and S is entropy. Entropy is also defined in stat mech as S = -k ln(W) where k is the Boltzmann constant and W is the number of microstates in a system.
What does this mean? A system in equilibrium doesn't always increase its entropy, rather it minimizes its free energy and one way to minimize free energy is to maximize entropy. Let's consider the three different states of H2O: at low temperatures, hydrogen bonds (i.e. potential energy) dominate free energy and the system exists as a low entropy solid. At intermediate temperatures, neither potential energy or entropy dominate and its a liquid. At high temperatures, the entropy term dominates and the water molecules exist far away from each other so as to have an extremely high number of microstates, and very little potential energy.
Your question "...what is the reason behind this tendency of a system to increase its entropy, and to lose its internal-energy" confuses two totally different situations. The entropy is maximized in a spontaneous process over its variables so that sum total of the the extensive parameters are kept constant. For example, the total energy and the total volume are kept constant meanwhile the inhomogeneities are smoothed out. The other case is when the internal energy is minimized assumes that the total entropy and the other configuration parameters, such as total volume, are held constant. Notice that this case refers to an adiabatic reversible process in which the total entropy of the system does not change.
You can read about this in Callen's chapter 5.1 of THERMODYNAMICS AND AN INTRODUCTION TO THERMOSTATISTICS" Here is a quote:
"The physical situation pertaining to a thermodynamic system is very closely analogous to the geometrical situation described. Again, any equilibrium state can be characterized either as a state of maximum entropy for given energy or as a state of minimum energy for given entropy. But these two criteria nevertheless suggest two different ways of attaining equilibrium. As a specific illustration of these two approaches to equilibrium, consider a piston originally fixed at some point in a closed cylinder. We are interested in bringing the system to equilibrium without the constraint on the position of the piston. We can simply remove the constraint and allow the equilibrium to establish itself spontaneously; the entropy increases and the energy is maintained constant by the closure condition. This is the process suggested by the entropy maximum principle. Alternatively, we can permit the piston to move very slowly, reversi- bly doing work on an external agent until it has moved to the position that equalizes the pressure on the two sides. During this process energy is withdrawn from the system, but its entropy remains constant (the process is reversible and no heat flows). This is the process suggested by the energy minimum principle. The vital fact we wish to stress, however, is that independent of whether the equilibrium is brought about by either of these two processes, or by any other process, the final equilibrium state in each case satisfies both extremal conditions."
You mention two "rivaling forces": maximization of entropy versus minimization of internal energy. I think of it this way:
Consider the Helmholtz energy $A$: $$ A = U -TS $$ Fixing the temperature $T$, we can describe a sponatneous change in $A$ as $$ dA = dU - TdS $$ and here I can see, where your argumentation is coming from: Minimization of $A$ (or a "spontaneous change", $dA \leq 0$) can be achived by maximizing $dS$ or minimizing $dU$. However, the tendecy to lower $A$ is only due to the increase of the entropy of the system and the surroundings - so to say a state of "maximum global entropy".
Take for example a system with constant $T$ and $V$. Then we can say $dS$ is the entropy change of the system and $-\frac{dU}{T}$ is the entropy change of the environment and both together tend to the maximum.
Another good example (see Atkins "Physical Chemistry") would be a spontaneous chemical reaction, where the change in Gibbs energy $dG$ is: $$ dG = dH -TdS \leq 0 $$ Analogous, we can debate the rivalry between the entropy and the enthalpy $H$. For an endothermic reaction, the change in the enthalpy is lager zero: $$ dH > 0 \,. $$ Since the reaction is spontaneous, $dG < 0$, it follows, that the entropy term $TdS$ "is stronger" than $dH$ (loosely spoken). Since I'm not the best with words, let me quote Atkins:
"Endothermic reactions are therefore driven by the increase of entropy of the system, and this entropy change overcomes the reduction of entropy brought about in the surroundings by the inflow of heat into the system..." (Atkins, "Physical Chemistry", page 117)
So this phenomenon can be explained with the picture of entropic driving forces.
This is an excellent question, and one that I feel is as philosophical as it is scientific.
For entropy, one must discard the definition of "disorder" and remember that entropy is simply a count of the number of states in which one may find a system. Take a deck of cards. All arrangements of a deck are equally likely. However, we assign a certain amount of "order" to one over the other, such as in new deck order. However, this new deck order is just one out of 52! (That's 52 factorial). It's far more likely to find the deck in what we consider to be a disordered state. You can think of it in the following manner. If I hand you a brand new deck, and I ask you to remove one card, and place it somewhere in the deck, there is only one position to place said card that retains this order, and 51 others that create a less ordered state. Thus, if moves of any system happen at random, it is the tendency for the system to find and wind up in states that are far more "disordered" to our point of view.
As far as energy, I still struggle with this as there isn't as simple a way to understand it. I guess I've reconciled it by disproving the opposite: systems continuously gaining more and more energy. This simply would not result in the universe in which we find ourselves. If systems were to continuously gain energy, or rather behave in such a way so as to gain energy, you'd end up with pockets of matter that would eventually experience some kind of nuclear fission as the energy in the systems would be too high (I suppose chemical bonds would have broken long before, but that's an issue when we are trying to show why minimum systems are what has to happen). I suppose you could also say that by minimizing your energy, you allow for other systems, the rest of the universe to explore more possibilities, and the the entropy-answer works.
