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1)

(a) We just learned that according to Rebbi Yishmael, "la'Par" comes to include the Par He'elam Davar. The problem with this is - that the Pasuk is written in connection with the Par He'elam Davar shel Tzibur, so why do is it necessary to specifically include it?

(b) The Torah needs to write it, Rav Papa explains, in order to learn the Din of Yoseres and Sh'tei K'layos with a Hekesh from it to Se'irei Avodas-Kochavim (as we shall see). We learn that the Par He'elam Davar requires the Yoseres and Sh'tei K'layos to be burned together with the Cheilev - from a Hekesh to Par Kohen Mashi'ach ("Ka'asher Asah la'Par ... Ve'asah la'Par"), where it is written explicitly.

(c) This creates a problem however - based on the principle 'Davar ha'Lameid be'Hekesh, Eino Chozer u'Malamed be'Hekesh' (so how can we learn the Se'irei Avodas-Kochavim from the Par He'elam Davar with a Hekesh, when the Par He'elam Davar itself is only learned from a Hekesh)?

(d) We have solved it - by Darshening "la'Par" to include the Par He'elam Davar (as if the Yoseres and the Sh'tei K'layos were written there explicitly, and were not learned from a Hekesh.

(a) We cite a Beraisa in support of Rav Papa. Quoting the Pasuk in Sh'lach-Lecha (in connection with the Se'irei Avodas-Kochavim) "Ve'nislach Lahem, ve'Heim Hevi'u es Korbanam ... ve'Chatasam ... al Shigegasam" (which is all superfluous). The Tana explains that "ve'Chatasam" pertains to the Se'irei Avodas-Kochavim "al Shigegasam" - to the Par He'elam Davar shel Tzibur.

(b) And he explains the connection between them - by comparing the former to the latter as regards the Korbanos (including the Yoseres and Sh'tei K'layos).

(c) We ask why Rebbi Yishmael finds it necessary to learn the Din of the Yoseres and the Sh'tei K'layos by the Se'irei Avodas-Kochavim from "ve'Chatasam", why can he not learn it from the Pasuk "ha'Chatas" (from which we Darshened 'Lerabos Se'irei Avodas-Kochavim'). Rav Papa answers that we may not be able to learn the Yoseres and the Sh'tei K'layos from the original D'rashah - because the Torah may well be comparing the Se'irei Avodas-Kochavim to the Par He'elam Davar, as regards Haza'os which are written specifically, but not as regards things like the Yoseres ... , which we only learn from a D'rashah.

3)

(a) Rav Papa confined the D'rashah "la'Par", 'Lerabos Par Yom ha'Kipurim' to 'es', 'be'Dam' and 'Tevilah'. According to Tana de'Bei Rebbi Yishmael however - it comes to include everything in the Parshah.

(b) When Rav Huna bar Nasan queried Rav Papa from there, he replied - that that is the opinion of Tana de'Bei Rebbi Yishmael, but that he holds like Tana de'Bei Rebbi, as we explained above.

(c) Tana de'Bei Rebbi Yishmael gives a Mashal to explain why the Torah ...

1. ... specifically mentions the Yoseres and the Sh'tei K'layos by the Par Kohen Mashi'ach but not by the Par He'elam Davar shel Tzibur - to a king who became angry with his close friend, and whose sin he minimized because of their special relationship (so it is with a Tzibur, with whom Hashem is particularly close).
2. ... refers to the Paroches ha'Kodesh in the Parshah of the Par Kohen Mashi'ach, but not in the Parshah of the Par He'elam Davar shel Tzibur - because on the other hand, when the majority of the king's subjects rebel against him, his majesty is shattered.

(a) Rebbi Meir learns in a Mishnah in Menachos 'Pigeil be'Kometz ve'Lo bi'Levonah ... Pigul ve'Chayavin Alav Kareis'. The Rabbanan rule 'Ein bo Kareis ad she'Yefagel be'Chol ha'Matir'.

(b) Resh Lakish maintains that Rebbi Meir's reason is not because he holds 'Mefaglin be'Chatzi Matir - but because he holds that a person's S'tam Machshavah generally follows on from his first Machshavah, and the Beraisa speaks when his first Machshavah was Pigul, and the second one, Stam.

(c) He learns it from our Mishnah 'Lefichach Im Nasan Kulan ke'Tiknan ve'Achas she'Lo ke'Tiknah, Pasul ve'Ein Bo Kareis', from which he infers - that the other way round 'Achas she'Lo ke'Tiknah, ve'Chulan ke'Tiknan, Pigul'. The author cannot be the Chachamim - who hold 'Ein Mefaglin be'Chatzi Matir' under any circumstances.

(d) And if Rebbi Meir held 'Mefaglin be'Chatzi Matir', then it ought to be Pigul whichever way round he thought. This proves - that Rebbi Meir's reason is because, in his opinion, the second Machshavah follows the first one, like Resh Lakish explained.

(a) Rav Shmuel bar Yitzchak establishes the author as the Rabbanan, and 'Kulan ke'Tiknan ... ', means 'ke'Tiknan le'Pigul', meaning - that the first Matanos were performed with a Machsheves Pigul, and the last one S'tam.

(b) And the Chidush is - that the second Machshavah does not necessarily follow the first one (to render it Pigul).

(c) We ask on him from the Lashon 'Kulan ke'Tiknan ve'Achas she'Lo ke'Tiknan' - which implies that the first Matanah alone would render the Korban Kasher. Otherwise, the Tana would have said 'Kulan ke'Tiknah Chutz me'Achas', or 've'Achas bi'Shesikah'.

(d) To corroborate Rav Shmuel bar Yitzchak's explanation, Rava therefore explains 'she'Lo ke'Tiknan' to mean - with a Machshaves Chutz li'Mekomo, and the Chidush is that a Machsheves Chutz li'Mekomo by the last Matanah of a Chatas Penimi negates the Machsheves Chutz li'Zemano of the first Matanos.

(a) Rav Ashi establishes 'she'Lo ke'Tiknan' to mean she'Lo li'Shemo. Either way, we can now infer from the Mishnah - that if The Kohen performs the last Matanah of the Chatas P'nimi ke'Tiknan, the Korban will be Pigul ...

(b) ... in which case the author cannot be the Rabbanan - who hold 'Ein Mefaglin be'Chatzi Matir'.

(a) We answer 'Aydi de'Tana Reisha Pigul ve'Chayavin Alav Kareis ... ', by which we mean - that the Tana could just as well have learned the Seifa by ke'Tiknan, and it would not be Pigul because 'Ein Mefaglin be'Chatzi Matir' and...

(b) ... the author is Rebbi Meir.

(c) The reason that he learned it by Chutz li'Mekomo or she'Lo li'Shemah is in order to balance with the Reisha (by Chata'os ha'Chitzonos) ...

(d) ... where he needed to learn Chutz li'Mekomo or she'Lo li'Shemah - to teach us that in spite of that, the Korban is Pigul, because the last three Matanos are not crucial to the Avodah, as we learned there.