In an old house, do I need a ground wire to install newer outlets, lights, and appliances?
GFCIs do not provide grounding and are not a substitute for grounding. They are allowed as a substitute for ground because they do a good job protecting people from electric shock.  This is worthless for equipment protection.  An ungrounded GFCI requires a sticker saying

NO EQUIPMENT GROUND

to put users on notice that the equipment will not be protected from ESD and cannot get a useful antenna ground.
In 2014 they changed the rules so you can now retrofit ground wires to older wiring.  Grounds can take any reasonable path (don't need to be kept with the cables) and circuits can share grounds.  So any given outlet only needs its ground to go to the nearest place with thick enough wire back to the panel.  That includes non-flexible metal conduit being used as a ground path, and the Grounding Electrode System (bare copper wire going off to ground rods).
With older houses, I advise assuming nothing about the Grounding Electrode System.  Nothing beats a physical inspection.  Valid GES paths are an Ufer ground (if it was poured into the concrete at build time), a water main clamp (on the utility side of the water meter; utilities are replacing meters with plastic  smart meters that do not conduct electricity) or 2 ground rods each 8' long... set at least 6' apart but preferably catty-corner on the house.  1 ground rod will suffice if it passes an expensive test.