To answer one question, poles are "north" and "south", and hence always come in pairs.

"To answer one question, poles are "north" and "south", and hence always come in pairs."

Exactly.

Well, one can have only North or South pole in an AC coil, but it is no longer a motor, it is just an electromagnet! The general idea of a motor is for it to spin. It's fairly ineffective as an enclosed electromagnet.

A Monopole AC electromagnet looks more like this.

It moves, but only in one direction for a short distance...

If a magnetic field starts from north pole it should end in a south pole to complete its path. Compare with electrical circuit where a current flowing from phase to neutral via a load(lamp/receptacle/machine). If circuit is broken(open circuit) current cannot flow except leakage current.