Hello, indeed the pattern reuse command only works on repeats (custom linear, circular).
The assembly symmetry feature creates a geometrically symmetrical part (i.e. different from the first one).
It's not a display problem, only both modes are visible (surface - solid)
If you hide the skeleton piece and the contents or geometric sets, you will only see the solids, in Catia's default color (grey*).
Yes, you can modify the parts either from the skeleton (diameter of the sphere, position of the sphere in height // floor, number of repetitions of identical parts, shape of the cuts, etc.)
And add mechanical functions to each unique part (I usually work with the assembly open for skeleton modifications, but since the assembly I open the parts in a new window to add mechanical functions. This is so as not to create links between parts of the assembly).
If I need an external ref I create it in the skeleton and then copy it with link in the room.
I would start by changing the center point of the sphere currently to X0,Y0,Z0 and give it the dimension // on the ground
I will create the reference for positioning and building the columns, as well as the circular repetition of every other piece.
Half shells, you have to deal with it, it's a particularity of CATIA, the same thing is found on cylinders, cones but actually on spheres even if it's a single entity. It behaves to the selection on the geometry as if there were two half-spheres.