I just wanted to know whether the following formula 3/2kT=K (ave) demonstrates the average kinetic energy per atom in a monatomic gas. And then if 5/2kT=K (ave) demonstrates the average kinetic energy per diatomic molecule. This comes from the fact that the average energy per degree of freedom is 1/2kT. Note k(lowercase) denotes Boltzmann Constant, and K (uppercase) denotes kinetic energy.
Yes, you are correct. The equipartition theorem breaks down at low temperatures when the energy kT is smaller than the energy spacing in a degree of freedom. It doesn't have enough energy to make that jump, so that degree of freedom becomes frozen out.