Based on some of your comments, I think what might be tripping you up is the first statement you started with:
From the Bohr's atomic model, it is clear that electron can have only certain definite energy levels.
and
...If suppose, we assume electron losses total energy, electron can't stay in any particular shell, as it would not have that particular value of energy.
That may be true for Bohr's atomic model, but Bohr's atomic model is wrong. And electron does not have to be in a particular, definite shell or energy level. Rather, any electron state is a superposition of states of definite energy level (energy eigenstates).
That means the expectation value of a hydrogen electron state is going to look like
$$\langle E\rangle = \sum_n |a_n|^2 E_n\text{,}$$
where $\{a_n\}$ are arbitrary complex values with $\sum_{n>0}|a_n|^2 = 1$ and $E_n$ are energy levels in increasing order. Because of the sum-to-$1$ condition, taking any portion along the other energy eigenstates will increase energy compared to the ground state.
In other words, even if the electron state does not have a definite energy, you still can't go lower than the ground state.
Suppose, I have a cup of hot coffee on the table. It will be continuously losing energy in the form of heat, but it stays on the table, though there was a energy loss. Now, all of a sudden, I take off the table, the cup of coffee converts it potential energy into kinetic energy to come down.
If you don't shake the table, the coffee cup will sit there, forever. Similarly, nothing perturbs the electron in an excited energy eigenstate, then it simply will never decay. It cannot: energy eigenstates are stationary; they do not evolve into anything other than themselves.
However, being completely without external perturbation is actually impossible. The uncertainty principle provides the electromagnetic field with vacuum fluctuations, which will perturb the electron even if nothing else in the environment does. In your analogy, this (or something else) provides the "shaking of the table" for the electron. Once the electron state gains even a tiny component in some other energy eigenstate, the state can evolve in time.
In other words, one can think of spontaneous emission as a particular type of stimulated emission where it's the vacuum that does the perturbing.
1.I understand that star is in Plasma state (all nucleus and electrons are not bound to each other and moving around freely)
While hydrogen only has one electron, all other neutral atoms have more than one electron. When one electron is removed, this is referred to as the "first ionization". Removing one of several electrons from an atom still makes it plasma. Also, the term "plasma" is used when a substantial fraction of the atoms are ionized, not necessarily all. So in the sun or other stars, there are still electrons bound to nuclei, as well as free electrons.
For these reason, in the spectrum below, one still sees lines from transtions between electron energy levels of atoms.
2.Photon is emitted when an excited electron moves back to lower orbit.
Yes, and absorbed when going to a higher level, that is why we see the lines in the above spectrum.
3.So in a star if electrons are not in any orbit then how can photons be produced?
The main reason is that gamma ray photons are produced in the core of the sun by hydrogen fusion to helium, and create a cascade of lower energy photons as they travel to the surface. Also, all materials emit black body radiation. The overall shape of the above spectrum fits well to a black body model.
Best Answer
The fire that is most difficult to see is Hydrogen burning in air, which is does with a pale blue flame making it almost invisible in daylight. Methanol is similar in some ways as well.