How many zig-zag patterns are there in a dog tooth leading edge?
Both terms (“zig-zag” or “dogtooth”) designate the same leading edge aerodynamic design, and are used interchangeably. “Saw-tooth” is also used to indicate the same leading edge pattern, yet it is also used in naming a specific trailing edge design (a “saw-tooth” trailing edge; see this paper which explores this effect: Saw-tooth, or, Serrated trailing edge
The number of “cuts” (or, extrusions of the leading edge of a certain wing section compared to the leading edge towards the root of the wing) are a choice of design.
The “dogtooth” (or “sawtooth”, or “zig-zag”) at the leading edge acts in a way similar to a wing fence ), inducing an effect on the relative airflow which acts to prevent span-wise flow (and also adds energy to the air flowing over any control surface in the area, increasing its effectiveness.
As there are aircraft with numerous wing fences, so can the dog-tooth extrusion be multiplied on each wing, however, it is a question whether there were any planes out there with more than three such points of extrusion.
See this question for more detail: Hawker Hunter Dog-tooth wing - Aviation SE
Take a look at these pictures: notice the “dog-tooth” / “saw-tooth” leading edge and “saw-tooth” / “serrated” trailing edge.