Table 7A phase 2 of AC = black so for 110 volt brown, black, green/yellow
Does that table not specify black only for phase 2 of a 3-phase supply though? With 110V CTE we don't have a 3-phase supply, only single phase, and the only color it lists for the live of a single-phase a.c. supply is brown. So while it might well be sensible within a larger distribution system to use two different colors to identify each live leg of the supply (and is certainly what I would do), I don't think that strictly speaking it would be compliant with the new scheme unless you sleeved brown at the terminations.
Either way, when it comes to the flex on U.K. 110V tools, although normally brown & blue everybody knows that each conductor will be at 55V (or 63V) to earth anyway, so there's really no room for confusion.
We tend to call them phase colours, but clearly also used with split phase
Indeed, and it would certainly make sense to identify the two outers of such a system throughout an installation. It's just that under the new scheme I don't believe that the strict letter of the regulations permits that (although in practice sleeving brown at terminations would comply and still allow easy identification throughout).
I am not saying it does not exist but 2 phase supplies must be quite rare.
Certainly they must be these days. I know that in a few U.S. cities there were still some 2-phase 4-wire supplies until quite recently (1990's perhaps?) which were maintained for things such as old elevator motors. There might still be a few left now, but no doubt they'll disappear entirely as old plant is finally replaced with new 3-phase gear.
I suppose with USA being 120 volt then 2 phases would be 207 volt so maybe a 220 volt AC would work, but using a 240 volt AC would have the same problem as in Algeria.
It's usually listed as 120/208V here, and certainly 230-240V motors can have a problem, allowing for the normal variation in supply voltage from nominal. Sometimes a buck-boost transformer is employed to run 208V equipment on 240V or vice versa.
Many straightforward resistance heating units are dual-rated for 208 or 240V use however, obviously with a lower rated output on the lower voltage. There are other heaters which are dual-rated for 240 or 277V, the latter being another standard utilization voltage here.