When the electron turns around the nucleus, does it discharge energy? And if it discharges energy, its energy is fixed at a certain level and changes only if it moves from one orbit to another or from one energy level to another
It is well established that electrons do not turn around the nucleus in atoms.
They are rather captive in resonance states that may not involve that they move in circle about nuclei. These resonance states are measured with the wave function of QM.
Their energy varies noticeably only if they move from one authorized level to another. If energy is communicated to them either by radiation of convection, they may jump to an authorized metastable orbital farther away from the nucleus, but this is temporary and they soon jump back to an orbital closed to the nucleus. When they jump back closer, they emit an electromagnetic photon to evacuate the energy now in excess.
This is how we can see matter, because these jumps towards orbitals closer to nuclei is what produces the visible light that allows us to see objects about us. When they receive light from outside sources, they jump to a farther away orbital, and when they jump back, they emit this light, which is why we see objects.
Each sort orbital jump in atoms towards the nucleus re-emits light at very precise frequencies. This is why we see the different colors.
If sufficient energy is given them, they may even completely escape the atom. When they are captured again, they emit an electromagnetic photon of very precise frequency.
Unfortunately, this type of long established information has become scarce in currently available intro textbooks.
If you could get older undergrad textbooks such as Halliday & Resnick "Physics", or Sears, Zemansky and Young "University Physics", you would get a complete and accurate overview of the basics.