What is the minimum radius and mass (if any) for such a structure to be stable? What is the ultimate future of such structure? Will the electron repellation always be stronger than any gravitational attraction? Even at any density?
It will never form a stable structure as both electrostatic and gravitation forces decreases at the same rate with distance. And if one dominates at some distance, then it will continue to dominate forever, as the charge to mass ratio of the star will still be same as that of the electron.