Well you should terminate all the earth connections together at the back of the plastic box, and have a fly lead from those terminations to the faceplate yes.
No, but you do need to connect the metal faceplate to an earth. If there is no earth wire available in the switch box you will have to search for one at the light or in a joint box under the floorboards.
Your plastic wall box is non conductive and does not require to be earthed , however, there may be an earth wire on a terminal that you should use.
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