How does the huge amount of kinetic energy of some fast object like a meteor or rocket etc. gets distributed into various kinds of energy like kinetic, sound, light etc after making an impact with another body. Is there a rule under which this happens or is it TOTALLY random, and if it is random then what kind of random process does it form?
It is not random. If the exact same meteor strikes with the exact same properties then the results will be mostly the same (barring a small amount of chaos).
So what is the distribution of energy. Well if you drop a ball on carpet and on a wooden floor it will make different sounds and it will bounce differently. So it is in the details of all possible interactions that define the results.
For movement you have work done, for heat you have thermodynamics and for sound you have acoustics. If you can simulate all the interaction of all these fields of physics then you can have an answer, but it will differ when the initial conditions change.
If you consider things on a microscopic level, the first thing you see are the atoms at the surface of the meteor colliding with the atoms at the surface of whatever it hits, lets call it "the ground". There will be a lot of these initial collisions, each one accelerating the atoms at the surface of the ground material. These atoms in turn accelerate the next layer of atoms, and so on. At interfaces between materials, the surface atoms on the first collide with the surface atoms os the second. And so on. In this way, the kinetic energy is distributed to many many objects.
Sound is generated because there are collisions with air molecules. Light can be generated if enough kinetic energy is deposited in a short time so that the material either catches fire, or electronic transitions occur in the atoms of the "target".