How can I limit scaling on one axis? When scaling or extruding a Gear's Edges, the edges  seem to scale down on the Z axis, in a way that is not level with the origin point of the edges:



Any other "default" Blender object will scale or extrude without scaling down on the Z axis:





How do I scale or extrude these edges without them moving to the center on the Z axis? I don't think it has to do with applying scale/location because all three GIFs in this question were produced at default size for each object.
The reason for this is because you have two edges selected, meaning your total selection has some height. Scaling by default will scale along each axis by the same percentage, thus it flattens some. To not scale on the Z axis, simply scale only on the X and Y axes. To do so, press S then Shift+Z to disable scaling on the z axis.