In physics everything that scientists say that they really know is incorporated in the standard model. As such the answers to most of your questions are unknown. For example we know that mass and charge exist because we can measure them. But we do not know why they exist. In the standard model the measured mass of particles are input parameters. Same for charge. That takes care of questions 1, 2 & 3.
(4) Physics says that charges communicate with each other through electromagnetic waves of "virtual photons".
No. Charges communicate through photons, as in light. Virtual particles are used to express static fields. Static charges generate static fields that we can measure. But since some scientists like to think that only particles can exist, they claim that static fields come from virtual particles. The other use of virtual particles, which is more real, is the particles that are spontaneously generated in vacuum. These often mask the value of the charge of an electron or proton and they get involved in other processes.
(5) If the magnitude of charge on electron and proton is same, then they must communicate with each other through electromagnetic waves of definite frequency. What is that frequency?
I never heard of this before. Atoms can emit light of all kinds of frequencies, so I do not think what you say could be possible true. Wire antennas propagate any frequency EM waves that you pump it with.
Perhaps you mean static and bare charges. In this case the scientists say that the charges feel each other via virtual photons of zero frequency. Since zero frequency photons contain no energy, invoking their use does not make sense to me. Better to use fields.
(6) How exactly electromagnetic waves from electron "attract" proton and vice-versa? How does
electromagnetc waves from electron to electron and proton to proton repel each other?
Same answer as above. We can speak of attraction or repulsion if the charges do not move. No wave in this case- just static electric fields, from which we can calculate attraction or repulsion.
(7) How does one magnet communicate with other magnet?
They do not if the magnetic fields are static. The magnetic fields just superimpose. However, if you move one magnetic, or if the magnetic field is generated by electrical winding with ac current, then photons are generated and Maxwell's equations determines the communication.
(8) What exactly gravity means?
Best answer is from General Relativity which represents gravity by curvature in space-time. So gravity is just space-time. But that is a representation and that answer may not be unique.
Has ever been "gravitons" detected? No
And how exactly this attraction through gravitons takes place? Unknown- just like attraction or repulsion via virtual photons, gravitational attraction is best represented by the gravitational field which has been measured. No need to invoke gravitons. For static gravitational fields, like the earths field, the gravitons would have zero frequency, and maybe zero energy, which does not make sense. But on the other hand, I have never seen an expression for the energy of a graviton. That does not mean that one does not exist.
9) What is the exact nature of elementary particle? What does this elementary particle contains? Whatever it may be, what keeps it together?
Almost by definition what makes a particle elementary is that we do not know its nature, except for measurable quantities like mass, spin and charge. In string theory particles can be the same as black holes. It is not know what keeps them together.
(10) Where from matter came? In other words, what was the cause of Big Bang?
Unknown. Some guesses from string theory and loop theory. Nothing verified. More below.
In spite of spazcon's remarks, I think you are as close as anyone to understanding where the fundamentals come from when you say "space density". The most fundamental theory is Loop Quantum Gravity, which I am not good at. In this theory, space and time are derived quantities, and I imagine that charge, spin, matter and mass will also be someday derived.
There is a theory for where mass comes from that is expressed by the Higgs field and its particle. This is the next step up from the standard model in which at low enough energies, the Higgs field breaks symmetry and all particles except photons experience inertia in pushing through the broken Higgs field. Its like upside down superconductivity. At high temperatures, the inertia of all particles goes to zero, whereas in superconductivity, at very low temperatures the flow of electrons becomes frictionless. The theory predicts the energy of the Higgs particle to be about 80GEV. However, it has not yet been observed going up to 110GEV at CERN. So the theory, and maybe even the concept, may be in error.
No real theory for anything else. But I can suggest a way to think about fundamental properties from string theory. There is a 26 dimemsional string theory of closed strings only. This is essentially the theory of the unified field in my opinion as it is a pure force field. Only force, no matter, and of course no mass or charge. So we have a theory in which the fundamental properties of particles you are interested in are zero.
The theory predicts a whole range of particles at different energies, including scalar and vector particles, particles of various spins, and particles that travel faster than light. These different particle properties can be derived from closed string dynamics, so it is understood where they come from. Space and time are background assumptions in this theory.
Physics is not sure that such a 26-d field exists, especially since it has faster than light particles. But lets assume for the moment that it is real.
Matter or fermions can only be created (mathematically) in 9, 10 (mostly 10), or 11 dimensions. There are several super symmetric string theories that describe fermions. One is 9-d; 4 or 5 are 10-d, and the 11-d M-theory has unified the others via duality.
So my guess is that the 26-d unified field ( which is not super symmetric) must transform into roughly 10-d in order to make matter. This can happen via compactification of the extra 16 dimensions. In the Big Bang, the resulting 10-d universe undergoes further compactification of 6 dimensions during inflation generating our 4-d space-time. According to Vafa, 3-d space comes from the opening up of closed strings. So space comes from strings.
Matter comes from compactification. It may or may not have mass at this time. String theorists also do not know where charge comes from. In the 10-d theories, they just assign charge to the ends of the open matter strings. Color charge, etc., are also assigned in this way.
So back to your space density. Since the 26-d theory does not have charges, of any kind, and the 10-d theories have them assigned, I postulate that these various kinds of charges came from compactification of the first 16 dimensions. I suspect that electrons, neutrinos, axions- all the light particles- also come from that first compactification, as the 10-d theories seem to predict quarks, but nothing lighter. And of course the quarks are a product of the final 6-d compactification as well.
So compactification, the curling up of higher dimensions into tiny undetectable balls ( first strings), is essentially a form of space density. Not 3-d space, but the 22-d compactified space. I would add configuration of compactification as important to our understanding.
Bottom line is that my intuitive feeling about how the universe works on a fundamental level, is the same as yours. But remember, its intuition, not scientific understanding. Science comes from intuition, with alot of mathemetics and measurements in between.
Hope this is of some help.