Outlet grounded by conduit - how do I add a second outlet with Romex?
If the box is grounded by the conduit, you can get self tapping grounding screws and screw one into the hole in the back of the box. Then wrap your ground from your NM cable around the grounding screw and tighten. Use the proper NM to box connector. Make sure you're not in an area that requires conduit.
In my humble opinion, the wiring shown in the lower box should be replaced if you're in a position to do so. It's old and will start breaking up if you mess around with it. As far as the grounding goes, if the box is grounded, you can replace the outlets with self grounding outlets and they will get grounded when screwing them into the box, or you can add a grounding wire to the box and attach it to the outlets.