Ground wire with 1/2 EMT Conduit
Not if you don't want to.  The EMT piping is itself a valid ground path, provided there is a ground path that is continuous back to the panel.  All my work is in EMT and I don't own any green wire. 

If you need to bond from the EMT to a ground wire, most likely there is a hole tapped for a 10-32 screw on the metal junction box, it may be sitting up on a pucker to give the ground screw some clearance. 

UK-style "ring circuits" are illegal in the United States and the wiring of the circuit should not be looped back to the panel.   

Sometimes conduit winds up being laid in a ring simply out of coincidence but the wires inside do not go in a loop.