How does Primary Sample Space Metropolis Light Transport work?
PSSMT operates directly on the space of random numbers that generate valid light paths. As such, mutations in the unit hypercube lose their physical interpretation since they do not have direct knowledge of the actual light path constructed. Recent research in rendering has shown that it is possible to bridge the gap between path space (that acts directly on the paths) and primary sample space (that acts on uniform variates) to some extent. See Bitterli 2018, Pantaleoni 2017 and Otsu 2017 if that interests you.
I am not entirely sure what you mean here, but typically an initial path of length $k$ will be formed using path tracing, and thus random numbers will be used along the way ($k+2$ if you are using BDPT). PSSMLT will mutate this path by acting only on the random numbers. Path throughput is indeed independent of the pixel but you only care about paths actually reaching the eye. At the end of the day, you are importance sampling paths according to their contribution to the final image, and luminance is what is commonly used.