Please note that unless otherwise indicated, we follow the explanation of Rashi. Consequently, our notes and comments do not necessarily have any bearing on the practical Halachah.

1)

(a) Shevu'os and Yedi'os ha'Tum'ah ...

1. ... Shabbos and Mar'os Nega'im all have in common - the fact that there are two cases specifically implied by the Torah and two cases that the Torah includes separately ('Shetayim she'Hein Arba').
2. ... have in common - the fact that both are subject to bring a Korban Oleh ve'Yored (meaning an animal Korban for a wealthy person, bird Korban for a poor person, and a flour-offering for someone who is very poor).

(b) The Tana is referring to a Shevu'as Bituy, which means - a Shevu'ah that a person makes voluntarily.

(c) The Pasuk writes specifically "Le'hara O Le'heitiv", which mean - either to suffer (such as by fasting) or to pamper oneself (such as by eating).

(d) The two cases that are specifically implied in the 'Shetayim' - both pertain to the future (that he will either fast and then doesn't or that he will eat and then doesn't); whereas the two that are included in the 'Arba' - pertain to the past (where he either swears that he fasted or that he ate, when really he didn't).

(a) 'Yedi'as ha'Tum'ah Shetayim' refers to someone who does not know that he is Tamei and eats Kodshim or enters the precincts of the Beis-Hamikdash. The 'Arba' - to where he knows that he is Tamei but not that he is in the Beis Hamikash or that he is eating Kodshim.

(b) We learn from the Pasuk "Vayetzav Moshe Vaya'aviru Kol ba'Machaneh ... " - the prohibition of Hotza'ah (carrying from the house into the street)

(c) 'Shetayim' constitutes the poor man (who is standing in the street) taking the loaf from the hand of the rich man (who is standing in the house) out into the street, and the rich man placing the loaf into the poor man's hand in the street, 'Arba' constitutes - the same two cases but with regard to Hachnasah (carrying from the street into the house).

(d)

1. The 'Shetayim' of Mar'os Nega'im comprises -Baheres and Se'eis (two appearances of Tzara'as) ...
2. ... whereas the 'Arba' comprises - Sapachas (which constitute the Toldah of Baheres and the Toldah of Se'eis.

(a) Regarding Yedi'os ha'Tum'ah, one only brings a Korban Olah ve'Yored - if there was a Yedi'ah to begin with, then he forgot at the time when he transgressed, and then he remembered again.

(b) If he was initially aware of the Tum'ah but then forgot and did not subsequently recall it, the goat that is brought inside, will atone for him until he remembers. This is the Sa'ir la'Hashem whose blood is brought inside the Kodesh to be sprinkled. Besides that, there is the Sa'ir la'Azazel (which was taken out of the camp and pushed off a cliff) and the goat of the Musaf (whose blood is sprinkled outside [in the Azarah]).

(c) 've'Yom ha'Kipurim Toleh' - means that Yom Kipur protects him from being punished until he remembers that he was Tamei and brings the required Korban.

(a) In the reverse case, if he was initially unaware of the Tum'ah but later realized that he had been Tamei - the Korban ha'Na'aseh ba'Chutz (as part of the Musaf) atones.

(b) He is not then Chayav to bring the Korban Oleh ve'Yored - because one only brings a Korban Oleh ve'Yored if there was a Yedi'ah at the beginning.

(c) The Tana Kama learns from the Pasuk (written by the Musaf in Parshas Pinchas) "u'Se'ir Chatas Echad, Milevad Chatas ha'Kipurim" - that just as the latter (the 'Chatas ha'Na'aseh bi'Fenim') atones where there is a Yedi'ah (at the beginning), so too, does the former (the 'Sa'ir ha'Na'aseh ba'Chutz') only atone if there was a Yedi'ah (at the end).

(d) If someone entered the Beis-Hamikdash or ate Kodshim without any knowledge at all of the Tum'ah - then the goats of the Musaf on Yom-Tov and of Rosh Chodesh throughout the year will atone for him.

5)

(a) The above is the opinion of Rebbi Yehudah; Rebbi Shimon disagrees by the goats of Rosh Chodesh, which, according to him, atone for - a Tahor person who eats Tamei Kodshim

(b) We might have otherwise thought that they do not - because, unlike the cases where a Tamei eats Tahor or enters the Mikdash, the Isur involved is not a Chiyuv Kareis.

(c) According to Rebbi Meir, all the goats atone for all of the above - with the sole exception of the Chatas ha'Na'aseh bi'Fenim of Yom Kipur, which atones for a Tamei person who knowingly enters the Beis-Hamikdash or eats Kodshim but who then forgets that he did (according to everyone).

(d) The point of so many Korbanos atoning for the same thing is - manifest in a case where someone transgresses between one and the other.

(a) Rebbi Shimon repeats the distinctions between the goats of Rosh Chodesh, of the Regalim and of Yom-Kipur - because of the She'eilah that the Rabbanan are about to ask him.

(b) When they asked Rebbi Shimon whether one could bring a goat that was designated for one of those days, but not sacrificed, on the other - he replied in the affirmative.

(c) And when they asked him how this is possible, bearing in mind the differences between them, he replied - that it does not matter, seeing as they all come to atone for Tum'as Mikdash ve'Kadashav.

(d) Rebbi Shimon ben Yehudah quotes Rebbi Shimon somewhat differently. He agrees that the goats of Rosh Chodesh atone for a Tahor person who ate Tamei Kodesh. But he then go on to say that the goats of ...

1. ... the Regalim - also atone for a Tahor who ate Tamei Kodshim, in addition to a Tamei who ate Kodshim be'Tum'ah or who entered the Beis-Hamikdash, without any knowledge at all.
2. ... Yom Kipur too - atone for both of the above in addition to a Tamei who ate Kodshim be'Tum'ah or who initially entered the Beis-Hamikdash without knowledge, but who then became aware of it.

(a) When Rebbi Shimon ben Yehudah permitted bringing a goat that had been prepared on one of the above days, on any one of the others, the Rabbanan asked him - how it is possible to bring the goat of Rosh Chodesh (which was designated specifically to atone for a Tahor who ate Tamei Kodshim) on Yom Kipur (which also comes to atone for a Tamei who ate Tahor Kodshim or who entered the Beis-Hamikdash)? ...

(b) ... to which he replied - that seeing as they all atoned for a branch of Tum'as Mikdash ve'Kadashav, it didn't matter.

(c) What atones for ...

1. ... Zadon Tum'as Mikdash ve'Kadashav is - Sa'ir ha'Na'aseh bi'Fenim (in addition to where there was knowledge at the beginning but not at the end).
2. ... all other sins, from Shogeg to Meizid, from Chayvei Asei to Chayvei Misos is - the Sa'ir ha'Mishtale'ach.

(a) The Sa'ir ha'Mishtale'ach atones for Yisre'elim and Kohanim alike - incorporating the Kohen Gadol.

(b) The Kohanim had a Kaparah of their own however - regarding Tum'as Mikdash ve'Kadashav, where the bull (brought together with the goat) atoned for whatever the Sa'ir ha'Na'aseh bi'Fenim and the Sa'ir ha'Na'aseh ba'Chutz atoned for on behalf of a Yisrael.

(c) Rebbi Shimon disagrees. He compares the blood of the bull of the Kohanim to the Sa'ir ha'Na'aseh bi'Fenim of Yisrael - inasmuch as, just as the latter, which was not accompanied by Viduy (confession) atoned for Tum'as Mikdash ve'Kadashev by means of the Zerikas Dam, so too, did the former atone for Tum'as Mikdash ve'Kadashav of the Kohanim by means of the Zerikas Dam ...

(d) ... leaving the Viduy made over the bull - to atone for all that the Sa'ir ha'Mishtale'ach atoned for by a Yisrael.