I agree with you that high temperatures can increase the kinetic energy of a matter. But one should not forget the basic fact that light is not a matter, but its just a form of energy. So it can only be converted into one form to another, such as heat.
According to laws of physics, Speed of light remains constant irrespective of the speed of source. One would observe the speed of light to be the same at all state (motion or rest). The speed of light only changes when it enters from one medium to another of different optical densities, a phenomenon called as refraction.
Now, this question can be answered from one of the points from above. As I have said, light consists of energy. I agree with you that some of energy is required to move a mass object. But, light particles, called as photons are massless (m=0). Then how would you expect to expend its own energy for movement.
Again, you are right. Yes, it is true that when light hits an object it transfers some of its energy to the sub-atomic particles present in the object. We can take example of the compton scattering effect. After hitting a charged particle, say electron, the energy of photon decreases and its wavelength increases ( such as those of gamma rays and x rays). I am not sure, but i think these again recombine with an other beam of light in appropriate proportion. In this way, energy will be conserved and would not contradic the law of conservation of energy.
I would prefer any expert in this forum to explain this thing more correctly.
And I'll answer your last questions soon, as its my time to lunch. So I am posting these all now