@Daniel I can't add to your question about succession and the Rebbe because of insufficient reputation but you may want to add this for the benefit of the community. If you say it in my name that's fine. The Rebbe has a niece, the daughter of his brother. Her name is Dalia Roitman who lives in Rechovot and last worked at the Weizmann Institute. She has two sons. So simply in terms of blood relatives with proper yichus, they exist.

@Daniel here's a link. Her sons names are Ariel and Daniel Yehoshua. jewage.org/wiki/en/Profile:P0610507389

@Daniel Ariel is 40 years old and Daniel is 37.

Ariel is 40 years old and Daniel is 37.