For the relativity thing, I'm just mentioning that the observer experiences the lightning strikes at the same time on the platform since they are stationary and equidistant from the strikes, while someone on the train will experience the strike at the front first since they are moving towards it, meaning the light needs to travel a smaller distance assuming the train is going relativistic speeds. I'm not sure about the light clocks thing you mentioned.
For blackbody radiation Im pretty much just mentioning the "Ultraviolet Catastrophe", where it was expected that as wavelength decreases, according to the wave model of light, since energy increases, there should be no peak wavelength and the intensity should approach infinity, which is not what was observed. I'm then just saying that Planck suggested that light may be quantised into photons, with energy E=nhf, meaning that since there are much less photons with high energies they don't produce as high an intensity, while at higher wavelengths the energy is just a lot lower so the intensity isn't as high. So pretty much the discrete energy packets thing with a little bit more detail and adressing the Rayleigh Jean issue, nothing about the quantum oscillators though.
Btw if I'm incorrect about any of this feel free to correct me, Im pretty much just saying how I understand it at the moment.