What are the connotations of "mi'Kol Chatoseichem"?
Oznayim la'Torah: It incorporates even Pesha'im (rebellious sins) on which the perpetrator did Teshuvah a. because Teshuvah (mi'Yir'ah) turns Pesha'im into Chata'im (sins performed be'Shogeg); 1 b. because sometimes the term 'Chet' has connotations of Meizid. 2
Tehuvah me'Ahavah turns them in merits.
Oznayim la'Torah: See for example, Sh'mos, 32:31 and Eichah, 1:8.
Does the day itself atone for Yisrael even without the Korbanos? If it is, why do we need the Korbanos?
Moshav Zekenim: Toras Kohanim says that the day atones even without the Korbanos. 1 The Yerushalmi (Yuma 8:7) explains that the day itself atones only at the end of the day. The Se'ir atones once it is sent to Azazel. R. Yanai holds that the day itself atones immediately - but only when there is no Mikdash and we cannot bring the Korbanos.
Sha'arei Teshuvah (4:3): Yom Kipur atones after Teshuvah. The primary Kaparah of Yom Kipur is after Teshuvah.
Why does it say "Lifnei Hashem"?
Moshav Zekenim: Yom Kipur atones only for "Chatoseichem Lifnei Hashem", but one who sinned against another person needs that person's pardon.
Why is Taharah mentioned twice, "Letaher Eschem? Lifnei Hashem Titharu"?
Sha'arei Teshuvah (4:17): "Lifnei Hashem Titharu" is the Mitzvas Aseh of Teshuvah. "Letaher Eschem" means that Hashem is Metaher us. This is for a Lav, but for Kerisus and Misos Beis Din, the Taharah requires punishments.
