Is the Planck law of radiation valid even for $T$ near absolute zero? Why can we be sure that the mean photon number inside a black body is zero for $T\to 0$?
There are no photons but harmonic oscillators inside a blackbody. At T=0, or rather at T=0.2K due to zero point energy, no photons are emitted since all of these harmonic oscillators are in the ground state. The number of photons emitted is zero.