Why excited electrons come back to ground or some intermediate level? Everything I have read did not explain it at all and just stated the fact. So WHY (what specific forces involved) excited electron spontaneously comes back to ground energy levels. Is it nucleus pulling electron inwards, so electron can not hold on in new energy level because part of energy was emitted while traversing orbital levels, or something else?
 A: It is the principle of minimum total potential  energy,  carried to the quantum mechanical level. Principles and laws are extra axioms necessary to use mathematical equations to model data and observations, and predict new set ups.
It is a basic observation that water flows downhill, if it can, after all. Electrons if a lower energy state exists will decay into it emitting the appropriate energy photon for energy conservation (another law).
A: Simply electrons want to minimize it's (potential)energy. Why it wants to minimize its energy? Because we have defined energy in such a way that when a system is at equilibrium, or steady state whatever you say, it's energy is lowest.
Now when we heat some gas and light comes out of it due to electrons spontaneously going the lower state from upper state. Now this may create a question like when energy is given then why not every electron takes energy, goes to higher state and rest there where it is, and resulting no emission. But when we speak of such situation then talking about one electron of a single atom is not the correct way of saying things, when the number of electrons is very high then it is possible that even you continuously give the system energy, some electrons will take up that energy and immediately afterward come downward giving up those energy in form of light. It is a statistical process.
Thus summing up electrons do tend to come to ground state, due to minimization of (potential)energy, but not every electrons and every second, there is a statistical description , that how many electrons will spontaneously come to ground state in what time.
A: Classically, if a charge accelerates, it will emit energy out into the electromagnetic field as radiation. This remains roughly true for quantum particles: the electromagnetic attraction between an electron and the nucleus accelerates them and therefore they tend to emit emit energy as particles of radiation (photons).
The idea of energy levels in an atom comes from ignoring the possibility of photon emission in the mathematics, keeping only the attraction between the electron and nucleus. In this picture, the excited states are indeed stable and never decay. Adding the possibility of photon emission makes all the excited states into "resonances", metastable states with "long" lifetime but that eventually decay. But adding this possibility does not change the possible ways to arrange the electron and nucleus in the absence of photon, and the (average) energies of such states also doesn't change much. Thus, no new states appear below the ground state, so the ground state atom cannot decay by photon emission. I.e. the ground state atom has no lower state to go to upon photon emission, so photon emission cannot happen even though the charges are constantly being accelerated.
Note that the full theory of photon emission is incredibly complicated: it requires quantum field theory and cannot be handled by basic quantum mechanics. Handling bound states (like atoms) in quantum field theories is also particularly difficult. I don't think a full treatment exists for arbitrary atoms, and finding one for even just hydrogen may be hard.
