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.
This will probably be downvoted for not bringing sources, but speaking as a chossid, it is impossible for a successor. Many people ask this question innocently, others with negative connotations, and try to give answers, but the true answer is that it is a question based on an assumption that there should be a successor. This assumption is false. The Rebbe continues to be the Rebbe of our generation, even if he is not alive. Has Breslov looked for a successor for R Nachman? Furthermore all the people mentioned above (R Adin Steinsaltz, R Yoel Kahn) are not suitable candidates at all, they are chassidim, not Rebbes (a huge difference).
As per your second question, there are many great Baalei Chassidus in Chabad, R Pinyeh (From Oholei Torah) R' Yeruslavski, the "Rosh" from L.A. (Ezra Schochet), among many others.