Since you have a metal structure and metal boxes, use metal conduit specifically EMT. Buy a bender and it's not that hard to work with. The EMT itself is a valid ground path, and you will not need to run a ground wire at all. Attaching the metal boxes and EMT clips to a metal building is icing on the cake. I have exactly this situation and I never run grounds, and there's never been the slightest doubt as to the reliability and ampacity of grounds.
Price 2-pole GFCI breakers for the panel you are using. You may be in for a shock. Your scheme of using MWBC will absolutely require a 2-pole GFCI. ThreePhaseEel's advice of "just run one more neutral wire and get out from under the exotic breakers" is very good advice.
Using the same circuit for both 120V receptacles and also a 240V receptacles, I'm not a fan. Generally if an American appliance wants 240V, it's because it needs that much power, and so it needs all of it. THHN is cheap and containers are not large, so just run an extra pair and be done with it.
Remember the 310.15 derate rules: you can have 9 active conductors in any conduit of any size (before having to upsize wire per the derate). Grounds never count, nor do neutrals in split-phase circuits (including MWBC)**. So if you run a 240V circuit, a 120+240V MWBC, and two plain 120V circuits, you are at 8. I often will lay two conduits next to each other if I expect to exceed 4 circuits.
** Neutrals don't count in split-phase because they only carry differential current: Suppose a neutral is carrying 15 amps, and one hot is carrying 20, that means the other hot is carrying 5. The heat from 2 wires carrying 15+5 amps is less than the heat of one carrying 20A, so those 2 wires get counted as one. Heat is a function of current squared.
You ask, why 9? In a 3-phase "wye" configuration, neutral doesn't count for the same reason. So three "wye" circuits add up to 9 conductors that count (12 wires in 3/4" EMT conduit since conduit=ground). At 277V you can put 277*20*9=49860W - frickin 50KW, enough to light up a CostCo.
Switches (only) can ground through the mounting screws
No need to run a ground wire to the switch. Presuming the switch has a metal yoke, it will ground via the grounding screws to the metal box (presuming it is grounded).
Is it grounded?
It's difficult to say whether the box is grounded. In 1960 all the boxes were metal, so that alone doesn't tell us anything. Merely being a metal box doesn't ground it; there'd need to be a wire or metal pipe (conduit) back to the panel.
However, you probably know cables come in black, white and optional red (and you're forced to use those colors for everything, which is not fun). I see no black and I do see blue.
Anytime you see nonstandard colors like that, you have to investigate whether this is an individual wires in conduit situation. If you see pipes entering the boxes with different numbers and combinations of wires in every pipe, that's conduit. Using different hot wire colors for different circuits, is also a common practice.
Conduit in 1960 was made of metal, such as EMT (Electrical Metal Tubing). If it's not flexible (and maybe if it is), metal conduit is a valid ground path in North America.
The proof of the pudding is in the eating; if a test light shows 120V from hot to ground, it's probably grounded.
Grounding receptacles: Heed what NoSparksPlease says!
Pay close attention to what NoSparksPlease says! Now, if the junction boxes are indeed grounded (e.g. via metal conduit as discussed above), here's how you can ground receps. #1: Run a wire to a ground clip or screw (often there's a hole tapped for a #10-32 screw in the back of the steel box). Or #2: Remember how I said you can ground the switch through the mounting screws? You can't do that with receptacles UNLESS:
If the receptacle's yoke (what the screw goes through) has hard face-on-face contact with the steel box, that is an acceptable grounding path. No rust. No paint. No little paper square that captures the screw. Of course now, you'll drop the screws, so buy spares (they're #6-32), but for another reason also:
With conduit, sometimes the screw will get hard to turn when it's 3/4 of the way down. This is the screw hitting the conduit pipe. Stop; you'll strip the hole out. Either cut the screw using the screw shear on your multi-tool (that's what that's for). Or just buy 1/2" #6-32 screws at the hardware store.
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As for grounding screws, you buy a bag of 50 of them (or generic 10-32 screws), and the (threaded) holes for them are in virtually every metal box, usually in a "dimple" so that the grounding screw can be screwed in even if the back of the box is hard up against a wall as mounted. They are not supplied with the box.