It's probably a good idea for both. A GFCI measures the difference between current into a circuit on the live wire and current out of it on the neutral; the ground wire just helps to make sure that in an electrical fault, the current isn't passing through you to ground. So a GFCI would be good in the places that current code calls for them: kitchens, bathrooms and outdoor circuits.
Same for the AFCIs: they help detect faults due to damaged wiring. With BX cable, that damage is less likely to be caused by driving a nail or screw through the cable than it might be with NM cable, but you still have the possibility of loose connections in your receptacles, or damage to electrical cords going to your appliances.
Another thing to consider: if you have older wiring, you may also have older breakers. If you're replacing some of them with GFCIs or AFCIs, you might think about having the rest of them replaced with newer breakers.
I agree, the /3 Romex is certainly intentional future-proofing in case you add a ceiling fan later. Unused wires should be capped, not wired to hot.
It looks like the Romex they used does indeed have a ground wire in it, and they have grounded the steel junction boxes, assuming corrosion has not damaged that.
However, note how the yokes (metal ears) of the switch and receptacle attach to the metal boxes, i.e. Only by the screws. The yoke does not bottom out onto the metal box, and where it makes contact is painted. The screw threads are not a legitimate grounding path.
So. Buy a couple feet of 12/2 NM cable and tear off the sheath and grab the ground wire. If you need more ground wire, strip the insulation off the other wires. Cut about a 6" length and pigtail it off the ground screw of the switch or receptacle. Then, unhook the ground wire(s) screwed onto the back of the box, and replace that with about a 6-8" pigtail. Now join both pigtails, plus the wire(s) you took off the screw, with a wire nut (red or green should be the best size). Shove all that into the back of the box.
Are those ground wires any good? The simple way is to use a 3-lamp tester and look for 2 yellow lights, or measure 120V between hot and ground.
The more conclusive way is to deliberately connect a duplex receptacle so the hot and neutral screws are actually connected to hot and ground wires. Then hook up a big load like a hair dryer or 1500W heater, measure the voltage across hot to ground, turn on the load momentarily, and measure the voltage again. Don't leave it on. It should sag only a few volts, about the same as it sags when wired correctly. Ground is not neutral and is not a substitute for neutral, but it is intentionally bonded at the panel, and this tests that continuity under load.
Almost any test between hot and ground will trip a GFCI device, since it is in fact a ground fault.
Best Answer
When you're extending old ungrounded circuits, Just randomly hooking up grounds higgledy-piggledy can create an interesting problem. I call it "Islanded grounds".
When a device has a ground fault, it's going to energize the ground wire. It's trying to return that ground fault to source (the panel and its N-G bond) so it can trip the breaker.
But imagine there is no ground wire back to source. If the ground wire just stops there, then it energizes the chassis of the machine.
But what if all the grounds in a circuit extension are connected to each other (but not the panel)? The "islanded" ground wire carries the ground fault around to all the other devices in the island. So now all their grounds are hazardous, even the cover plate screws on the light switch! That's the very opposite of a safety improvement!
So someone extending a non-grounded circuit might do just what you see. I'd prefer to coil it up and insulate it, myself, for the happy day the original wiring is replaced.