What does the word "Ach" come to teach?
Rashi: It precludes from a Kaparah someone who does not do Teshuvah. 1
Ramban, Moshav Zekenim: It does not preclude anything, but comes to substantiate the statement, as if it had written 'Achein' - in truth. 2
Hadar Zekenim: The other Yamim Tovim are called Mikra'ei Kodesh to eat, drink and get pleasure. These are forbidden on Yom Kipur. It is called Mikra Kodesh only to offer a Korban, and be forbidden in Melachah. Also refer to 23:35:1:1.
Ibn Ezra: Since it is a Mikra Kodesh, it is a day of Simchah, like we find "Lechu Ichlu Mashmanim
What does "v'Inisem es Nafsoseichem" incorporate?
Targum Yonasan: It incorporates a prohibition against eating, drinking, washing (bathing), anointing oneself, wearing shoes and intimacy. 1
We rule that only the first two are min ha'Torah. The other four are only mid'Rabanan. See also Ba'al ha'Turim.
Why is Yom Kipur on the 10th of the month?
Moshav Zekenim, citing R. Eliezer of Garmaiza: This recalls the merit of Avraham, who was tested with 10 tests, and circumcised himself on the 10th, and Yitzchak's merit, that [his Akeidah] was Avraham's 10th test, and Yakov's merit - he was blessed with "v'Yiten Lecha" (Bereishis 27:28; there are 10 words in the verse 1 ), and who said "Aser A'asrenu Lach" (Bereishis 29:22).
Why do we consider only the first verse? He was blessed in other verses with other numbers of words (27:29, 28:3,4, 13-15)
Why does the Torah not mention Korban regarding Yom Kipur?
Moshav Zekenim, citing R. Eliezer of Garmaiza: The Chelev and blood that are diminished through the fast, is considered to Hashem like bringing all the Korbanos - "Zivchei Elokim Ru'ach Nishbarah" (Tehilim 51:19), and is even dearer, for Korbanos are [offered] via one's money, and the fast is via his body. 1