amircan yeshivish
I’ll only comment on the disputed ones and will try to avoid loshon hora and machlokes but as someone over 45 I know the answers to almost all
(3)It was only said to be three in my days, then two others were added after they got divorced. And no, not every shidduch that RBS was shadchan for ended up in divorce.
(7) It’s question of whether some bochurim went to the rebbe for a yartzeit or for Shavous. Either way he retraced his resignation. According to Reb Moshe Pivovitz from the few people to have learnt by Rav Schach in Karlin to still be alive ten years ago, most of the Yeshiva was not chasidim to begin with
(10)Binyan olam was written anonymously for good reason. They say Rav Hutner threw it on the floor when he first saw it. Alleging authorship to someone would put that person into question in general
(13) Probably no one. Toras Chabad is too vast for someone to learn all of it unless he learns it on a daily basis. Rav Hutner was a chavrusa of the Lubaivtcher rebbe in Toras Chabad before he became rebbe. He then become a strong opponent of his . Of note the Lubavicher rebbe has no other known chavrusa