First things first: do you see any orange wires, or wires with orange tape on them? If so, you definitely have what is known as a "high leg" or "wild leg" delta system -- based on your voltages, I believe you have this, which was used historically to supply both 3 phase 240VAC and 1 phase 240/120VAC to mixed occupancies, as in the illustration below (courtesy Wikipedia/Gargoyle888):
In this system, the secondary center tap forms the split-phase neutral, with the A and C phases as the normal 120V "hot" legs in the derived split-phase supply, and the "high" or "wild" leg, while normally the B phase (this is from 408.3(E)(1) in the NEC, by the way) sits unused as it has 208V to the neutral on it.
Now that that's explained, to answer your questions in turn:
Typical 6/4 service entrance quadruplex uses PE (XHHW) insulation rated to 75°C and is thus limited to 60A. If you can confirm that the service entrance uses XHHW-2 (XLPE) insulation, though, you can run it up to a 90°C rating, which gives you a 70A (some sources say 75A) max ampacity. The XHHW or XHHW-2 designation is part of the markings on the insulation, by the way.
Is the ALU#4 cable type SE(R) or type USE (also called SEU) cable? SE(R) cable can be used for feeders indoors provided that the bare conductor in the cable is used only for equipment grounding purposes, as per 338.10(B)(2), or if all wires in the cable are individually insulated, as per 338.10(B)(1). However, USE/SEU cable cannot be used for indoor feeders as per 338.12(B)(1), as its insulation is not flame retardant.
Connect the feeder cable to the feeder breaker (either 60A or 70A) in the three-phase panel; connecting a load directly to panel busbars is simply not cool.
While your thought of making it so the subpanel main breaker trips before the feeder breaker in the main panel is appreciated, selective coordination is a much more complex piece of work than simply using a smaller subpanel main breaker than the feeder breaker. Here's an article on the topic if you want a taste of the gory engineering details that you'll have to work out to do this. You can use 60A breakers for both the feeder and the subpanel main, by the way; however, there are no guarantees as to which breaker trips first into a bolted fault (hard short).
You can tap the A and C legs from the existing 60A three phase breaker in the main three phase panel and use them to feed the subpanel; this is the most cost effective approach, and doesn't require any inspection of the service entrance conductors.
Finally, keep in mind that 60A is a very limited amount of current for a single dwelling unit. It can be managed, though, if you are able to run the heavy single loads (dryer, range/stove, hot water, and HVAC) using whatever fuel gas supply is plumbed to the building instead of using electric heavy-load appliances, or if the heavy loads for that dwelling unit are run directly from the three-phase supply -- although in some high leg services, the B phase is limited to a small fraction of the total load, which can make this infeasible.
Is there a reason the utility won't simply replace the obsolete high leg delta service with either a 240/120V split phase or a 208Y/120V three phase wye service?
Addressing the conduit problem, the neutral, and the balancing issue:
I would use conduit bodies instead of elbows, unless elbows are the only thing that fits in the space. In any case, make sure you have no more than 360 degrees of bends between your pull points!
The neutral coming from an overhead pole is on the bare wire in a triplex or quadruplex cable, just about always.
Phase balance isn't typically worried about in high-leg deltas; it's a concern in a wye system due to unbalanced currents flowing through neutrals, which need to be sized appropriately to carry it.
Take the subpanel back and get another one, with an eye toward two features:
- Auxiliary ground bus included, not an extra-cost add-on
- lots and lots of spaces. Right now in your construction, spaces are dirt cheap; regrets are expensive. Especially if drywall is involved.
Also look for
- being bundled with useful "bonus" breakers
- being a quality type (Siemens, QO, GE Qline, CH)
- having sensibly priced AFCIs ($40ish) and GFCI/AFCI combos ($55ish). Can't use brand X breakers on brand Y panels; that's not brand loyalty but a matter of proper fit.
- same type as your main panel (if you care)
It does not matter what the panel ampere rating is, as long as it is >80A because that is the breaker to use with your 75A 2/2/2/4 cable.* There is nothing wrong with getting a 200A subpanel for instance, as long as it has a plentiful supply of breaker spaces. Headroom increases safety and also allows for easy upgrades (just replace the cable/breaker).
The subpanel does not need a main breaker, but if it's cheaper (with bonus breakers) to accept a panel with one, that's fine.
* 75A -- yeah, the advice you got was that wrong. Never take advice from big-box again. In fact let's get you shopping at a proper electrical supply house. Most are locally owned businesses, and most will be happy to deal with you at sensible prices. Be honest with them that you're sick of dealing with big-box and their limited selection**, terrible advice and you're heard electrical supply prices are actually better on most things.
** I suspect that's why they put you into 2/2/2/4 Al.
Best Answer
The small appliance requirement is for the kitchen counters 2 as 20 amp circuits. If you want you can add a circuit for the bar but it would not be required.