Supply an Arduino via the magnetic energy created by a mains wire?
No, wrapping a coil around a straight wire does not make a transformer.

To derive electric power from a magnetic field, the field has to go "thru the hoop" of a coil of wire.  The magnetic field around a straight wire is circular around that wire.  If you wrap another wire around the first wire, that second wire is essentially following the magnetic field, not making a loop for it to go thru.