These are relationship lines showing parent/child and constraints. Go to 3DView > View > Properties (N) > Display and uncheck Relationship Lines

My understanding is that a fractal is a set or shape that has stays the same under scaling. A circle stays the same under rotation, but if you zoom infinitely close to a boundary of the circle, it looks like a line. A fractal, on the other hand, when zoomed into, looks the same or similar. The Fractal Geometry of Nature has lots of technical details. The Computational Beauty of Nature has a somewhat more accessible section on fractals.

Generate Fractal makes a bunch of copies but they are all in the same place. So, initially, you don't see any difference in the 3D view. Check out the Outliner. Once you move the first generation copies you will see lots of structure.

Select the original base object. Press "]" to move deeper in the fractal. Press "[" to move shallower in the fractal.

Yes! As of 2020-07-09 there is a new zip file for 2.8x. It has been tested and verified on 2.80 through 2.83, as well as 2.90

As of 2022-06-01 now supports blender 3.1.2 as well