1: Sorry about that, the default 20,000 is to make it look nice on computers but I should probably drop it a bit for phones, that's reasonable.
2: Yeah this part is important and cool and not entirely obvious until you solve the differential equation. I did a 3D simulation of a somewhat related situation (Thompson problem) once. But it would be very interesting to figure out if there is a 3D potential function that gives uniform density in the same way as the Ginibri (Q(z) = |z|^2) potential. Good idea for future work :)
3: Make sure you try the lemniscate potentials as well which are not rotationally symmetric. I want to try adding even more potentials in the future but these two families are those which has been subject to the most research.