Should a metal back box for a switch light be earthed to a plastic face plate?

The plastic faceplate - if earthed within the faceplate will then 'earth' the box via screws that hold the plate in place UNLESS the back box has plastic receiver screw mounts (the female part of the thread) then there is separation and so it is protected another way - to answer your question - does the plastic faceplate need to have a fly lead to the metal back box? no, but it wouldn't be unreasonable to fit one anyway, though it wouldn't be a requirement in line with the bs7671.

The CPC should be connected to the metal back box . The plastic switch does not need a CPC connection. You would only require a CPC connection to a class 1 metal switch.

The metal backbox should be earthed with the earth wire in the supply cable.The plastic face plate need not be earth but if the faceplate is metal,the metal back box and the metal faceplate should be earthed accordingly.

A "Flush" metal backbox (i.e. flush with the wall finish e.g. plaster) will need to be earthed using the CPC of the supply cable but there is no need to have a fly lead to link across to earth a plastic face plate as it is non-conductive. The screws that secure the plastic faceplate to the backbox are classed as exposed conductive parts (if you can touch them and they are metal) so they need to be earthed but this is usually achieved by the earthing of the backbox which in turn will earth any metal such as the faceplate screws that it comes into contact with.