Should I connect or remove the paper insulation layer on wires when installing a new plug?
Cloth and paper do not conduct electricity, so there is no use connecting them to any terminal. Simply snip them back.  

If you bought 12/2 cable which is line cord specifically made to be cordage, it won't have a ground.  

If you bought 12/2 NM cable, that will have a ground, but it is NOT to be used as cordage and should not be connected to a plug.