The single pivot uses one pivot that joins the swingarm to the frame: the wheel swings in an arc around that point. It is the most simple, reliable and cheap-to-maintain system. Its limit is not pedalling (that is a myth) but that it has less freedom to shape anti-squat and the axle path than multi-pivot systems. It is the foundation of the whole family of systems.
If you understand the single pivot, you understand 80% of the rest: almost all of them are variations that add pivots to it to gain fine control.
Picture a door: it swings around a single hinge, always the same arc. The single pivot is that, with the wheel in place of the door.
The rear swingarm is a rigid piece anchored to the frame by a single pivot. The wheel cannot take any path other than that arc. The leverage ratio can be shaped with the rocker that pushes the shock — but the axle path and anti-squat are tied to where the pivot sits.
No: it is a myth. Well designed, its anti-squat is adequate. Its limit is the freedom to shape complex curves.
The swingarm is one rigid piece, with no articulated pivot between the main pivot and the axle. Even if it has a rocker for the shock, it is still a single pivot.
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