YYtz,
1. Rav Kook saw the positive side of Chassidut and was himself a descendant of the Baal haTanya. However, he also had strong criticisms of its attitude towards rebbes. I never heard that he considered himself tם be a gilgul of RN.
2. See Mishpat Cohen 147 in which Rav Kook dounts that there is any mitzva to go to a tzaddik’s grave. Furthermore, he states that going to see one’s rav is only a live rav (Rav Tuchichinsky brings down in Gesher haChaim 2:25 that one who talks to a dead person may be over on derisha el hamitrim and if he prays to him on avoda zara).
2. Rav Tzvi Yehuda (his only son) certainly did not almost become a Breslover. In fact, he was very much a mitnagged and said that his Torah is a continuation of the Gra’s. In any case, almost never counts except in ring toss and hand grenades.