1)
When did Moshe ascend Har Sinai to atone for Yisrael's sin?
1.
Rashi: On the 18th of Tamuz 1 until the 29th of Av, when Hashem forgave Yisrael for the sin of the 'Eigel. 2
1
In Sh'mos 33:11, Rashi explained that Moshe ascended Har Sinai for the second time on the 19th of Tamuz! See Sifsei Chachamim there.
2
Rashi: The atonement was only complete however, when, after ascending the Mountain for the third time on Rosh Chodesh Elul, he descended with the second Luchos on Yom Kipur, and Hashem forgave them with Simchah and announced 'Salachti ki'Devarecha!' - which explains why Yom Kipur became the day of atonement.
