Refractive index, wavenumber, and wave impedance of the PEC that a plane wave is normally incident on
Wave number is a property of a wave, not of the medium it travels in. It makes no sense to ask what is the wave number of a material.

No electromagnetic wave can travel in PEC (because its conductivity is infinite and the skin depth of any wave reflecting off it is 0), so it makes no sense to ask what is its refractive index.

Similarly, since no electromagnetic wave can travel in PEC, it makes no sense to ask what is the wave impedance in PEC. (Your result that the impedance is zero may be useful for determining the phase shift of the reflection)