Why does everyone learn Pirkei Avos between Pesach and Shovuos and only “some” have the custom to learn them also in the summer months?
Based on Biurim Lepirkei Avos in several places (farbrengen of Shabbos parshas Nizovim Vayelech 5736) and others

Why did the angles think that they deserve the Torah more that humans?
Based on Likutei Sichos Vol. 18 pages 28-34 and others

Yisro: Why is it incumbent on a Yid to influence gentiles to fulfill their seven Noahide laws? Also: 1.   Why isn’t it enough to spread Yiddishkeit amongs Yidden? Why do we also have to encourage the gentiles to do their Mitzvos? 2.   Why did the Rebbe start this campaign in these last decades? 3.   What… Read more »

Did the Yidden say “Naase venishma” before or after the giving of the Torah?
Based on Likutei Sichos Vol. 21 pages 138-145 and others

Why do we Toivel Keilim that were bought from a non-Jew? Why dont we Toivel the Keilim that we sold to the goy before Pesach? Why do we eat Milchigs (dairy) on Shavuos?
Based on Likutei Sichos Vol. 18 pages 363-370 and others

Siyum on Masechte Nazir which is discussed in Parshas Naso
Based on Likutei Sichos Volume 18 Pages 63-75

Will the Real Meraglim Please Stand Up?
Based on Likutei Sichos Vol. 33 pg. 78-84, Sefer Hasichos 5747 pg. 448-461 and others.

Will the real Korach please stand up?
Based on Likutei Sichos Vol. 18 pg. 187-195, Sefer Hasichos 5748 pages 499-511 and others

Will the real Moshiach please stand up? (part 1)
Based on Likutei Sichos Vol. 18 pages 271-284 and others

Moshe Rabbeinu didn’t know the answer?!
Based on Likutei Sichos Vol. 13 pages 93-98 and others