who is the closest person today to being the successor of the Lubavitch Rebbi?
i.e. who is the biggest (greatest scholar) Chabad Rabbi to ask questions to about Chabad issues.
Rabbis Moshe Kotlarsky and Rabbi Yehuda Krinsky currently head the Lubavitch institutions. See more here, including a discussion of their succession plans.
As for which Chabad Rabbi is known as the greatest scholar today, I don't know but the one who comes to my mind immediately would be Rabbi Adin Steinzaltz, whose name had been briefly floated by some outsiders as a great choice for an eighth Lubavitcher rebbe.