LaTeXdraw-com, the result of your code is really pretty beautiful. The rotation of the cores also improved a lot and made the illustration closer to the physical implementation of magnetic core memories. I made a small change over your code so that the direction of the magnetic flow of a core is determined randomly and not according to their position, since ...
Here is my attempt for the first part of your request:
\node [draw, cylinder, cylinder uses custom fill, cylinder body fill=white, shape aspect=4, rotate=0, minimum width=2cm, line ...