Short answers, pulled from the story.
Michael Faraday gave the first demonstration of rotary motion on the 3rd of September 1821 showing how current gives rise to circular magnetic fields around wire. This event took place in the basement of the Royal Institution where a free-hanging wire dipped into a pool of mercury rotated around a permanent magnet.
German-Russian Moritz von Jacobi created the first real useful rotating electric motor in May 1834 developing remarkable mechanical output power setting world records improved four years later in September 1838. This device represented a significant advancement over earlier experimental motors like Barlow's wheel which remained unsuited for practical application until late in the century.
The motor contains two primary mechanical parts: a rotor that moves and a stator that remains stationary. The rotor typically holds conductors carrying currents while the stator surrounds it with field magnets or electromagnets made from wire windings around a ferromagnetic iron core.
BLDC motors typically achieve efficiency above 85% reaching up to 96.5% while brushed DC motors operate at 75, 80% efficiency. These motors eliminate mechanical rotating switches replacing them with external electronic switches synchronized to rotor position to significantly exceed the life of brushed DC motors with commutators.
Nikola Tesla independently invented his induction motor in 1887 obtaining a patent in May 1888. He presented paper A New System of Alternate Current Motors and Transformers to the AIEE describing three patented two-phase four-stator-pole motor types including reluctance synchronous and true synchronous motors which enabled long distance power transmission systems.