Ehh... while I see your point, I take exception with the wording. I'm sure this is obvious to most, but it's extremely common to use the phrase "single supply" to refer to Gnd/Vcc supplies, and "dual supply" to refer to V+/V- supplies, where Gnd is presumably in the exact middle to support symmetric AC signals.
Yes, but that's nothing to do with the op-amp, that's the circuit. Of course in a single supply circuit you either have to create
a virtual signal ground (or sometimes get away with using the negative rail as signal ground), but the same opamp can function
in either context.