Question #1: In Pesachim (58b) we say 'what is the source that nothing may precede the [morning] Tamid? It says "ha'Olah" - the first Olah.' We should learn from here!

Suggestion: That refers to Nedarim and Nedavos, and here it refers to Musafim. Musafim have a fixed time, and Nedarim and Nedavos are possible on every day, so they are Tadir.

Rejection: In Menachos (49a) it explicitly brings "ha'Olah" regarding the Mishnah that Temidim are not Me'akev Musafim;

It says "what is the case? If he has [lambs for both], and [it teaches about] offering first (the Tamid need not be first, this cannot be, for) a Beraisa teaches 'what is the source that nothing [may precede the Tamid, and it learns from ha'Olah]'!

Question #2: Bava Kama (111a) is more difficult. It expounds that "Milvad Eil ha'Kipurim" implies that money is first (one may bring his Asham for Gezel ha'Ger only after giving the money to the Kohanim);

[The Gemara] asks that if so ("Milvad" connotes before), "Milvad Olas ha'Boker Asher l'Olas ha'Tamid" should teach that Musaf is first, but a Beraisa teaches 'what is the source that nothing...'!

It should have asked from our Mishnah here, for just the contrary, it expounds that since it is written "Milvad Olas ha'Boker", this teaches that Temidim are first!

Implied suggestion: We need the verse here for a Tzibur that has enough [lambs] only for Temidim or Musafim (but not both of them. Even if the Musaf is for today and the Temidim for tomorrow, we save them for the Tamid - Tzon Kodoshim.)

Rejection: Our Mishnah does not discuss this, similar to the Seifa, which teaches that Dam Chatas precedes Dam Olah!

Implied suggestion: One verse teaches l'Chatchilah, and one teaches that it is Me'akev.

Rejection: [The order] is not Me'akev, like it says in Menachos (49a).

Answer #1 (to Question #1): '"Ha'Olah" - the first Olah' teaches that it is first for Haktarah, and the verse here teaches that it is first for Shechitah, for "Ta'asu Es Eleh" discusses [offering] blood.

Support: Now it is fine that in Menachos there, it brings "ha'Olah" to teach that even for Haktarah, which our Mishnah did not teach, the morning Tamid is first.

Answer #2 (to Question #1): [The questioner in Pesachim thought that it is Me'akev. Therefore he brought from the Beraisa,] because the expression "nothing may precede" connotes that it is Me'akev more than our Mishnah [does].

Answer #1 (to Question #2): Now it is fine that in Bava Kama (111a) it does not bring our Mishnah to prove about "Milvad Eil ha'Kipurim" that the money is not brought first;

Really, the money is first, since Kesef was written first, and afterwards the ram;

However, here we discuss offering the blood. The verse means as follows. "Milvad Olas ha'Boker", for which you already offered the blood, offer these [Musafim];

However, Haktarah [of Musafim], which is written before the verse "Milvad Olas ha'Boker", is before [Haktarah of] the Tamid, for all the verses beforehand discuss Haktarah, for they say "Isheh Rei'ach";

Therefore, we need to bring from "ha'Olah". Even though Haktarah of Musafim is written before Milvad Olas ha'Boker, Haktarah of the Tamid precedes them;

Likewise here, even though Kesef is written before "Milvad Eil ha'Kipurim", it can be that the ram is offered before [giving the money].

Question #1: The verses before Milvad Olas ha'Boker discuss also Avodas ha'Dam, like it says above "v'Sa'ir Chatas Echad Lechaper Aleichem", and Kaparah is through the blood!

Question #2: Why don't we learn Haktarah and blood from each other?

Answer #3 (to Question #1 - R. Chaim): We need "ha'Olah" for Chavitei [Kohen Gadol]. We cannot learn from "whatever is more Tadir", for it is offered every day, just like the Tamid.

Support: This is proven in Yoma (34a). It says that limbs are offered before the Minchah, for a Beraisa teaches "what is the source that nothing...", and Rava said that it discusses Minchas Chavitim;

If it were Minchas Nesachim, I already know [that the limbs are first] for it says "Olah u'Minchah";

We need the verse here ("Milvad...") to teach about everything Tadir, that it comes earlier.

Objection (to Answer #3): However, this does not help at all more than if we would say that ha'Olah is needed for Nedarim and Nedavos! (Still, why does Menachos (49a) bring "ha'Olah" to teach that the Tamid precedes Musafim?)

Question #3: Why don't we derive that Temidim precede Musafim because it says about the Tamid "ba'Boker"?

Something about which it says "ba'Boker" should precede Musaf, about which it is written "ba'Yom", which connotes that in the middle of the day, like we expounded there ba'Yom - after!

We say also in Pesachim (58a) that Musafim are offered in the sixth hour, and then it is not morning!

Poor Answer: If not for "ha'Olah", we would delay Haktarah of the Tamid until after Haktarah of Musaf, like it connotes in Bava Kama (111a), since it says Milvad;

We would establish "Ta'aseh ba'Boker" regarding Avodas ha'Dam.

Question: Still, it is difficult, since it is written ha'Olah to exclude that reasoning, why do we need "Milvad" to teach that Temidim precede Musafim for Avodas ha'Dam? We should know this because it is written about the Tamid "ba'Boker", and regarding Musaf [it is written] ba'Yom!

Remark: Here it is fine (that we question the question), for the reason is explicit in the Mishnah.

Question: However, in Megilah (2a), it is difficult. It asks "[why do you ask] what is the source? It is like we will say below, Chachamim were lenient...!"

So what [if it is taught below]? Is that a reason not to ask "what is the source?", since the reason is not explicit in the Mishnah!

Implied question: Why doesn't it say that the reason is because [Asham] atones?

Answer: It is because there is Asham Nazir and Asham Metzora that do not come to atone, rather, to be Machshir (enable counting Nezirus Taharah, or permit eating Kodshim), like it says in Menachos (4b).

Implied question: Regarding Chatas, it says the reason that it atones, even though there are also Chatas Nazir and Chatas Metzora that do not come to atone, rather, to be Machshir, like it says above (9b) "these [Chata'os] are [like] Olos"!

Answer: The reason that it atones is not enough, because Todah and Eil Nazir are more Kodesh [in one respect], that bread must be brought with them, like it says in the Gemara (89b).

Explanation: Chatas ha'Of is different. The Mizbe'ach gets only its blood. (Ma'aser has two matters that are Kodshei Kodoshim, i.e. for the Mizbe'ach - blood and Eimurim.)

Since [Ma'aser] is before Chatas ha'Of, all the more so it is before Olas ha'Of, for Chatas ha'Of precedes Olas ha'Of, like the Mishnah proceeds to teach. So Rashi explained.

Question: The reason is fine for blood, but why do Eimurim of Ma'aser precede Olas ha'Of? [The Mishnah] says that [Ma'aser Behemah] has precedence in every way, like is proven in the Gemara!

Answer: Perhaps regarding Eimurim, the reason that it is a kind of Zevach suffices.

Implied question: Why didn't it say the reason because its blood is put on the four Keranos, like it says regarding Asham?

Answer: Since Dam Olah comes to due to [a Korban] that is Kalil (totally Huktar), like it says in the Gemara, the reason of four Keranos does not suffice.

Implied question: [The Mishnah] said that Dam Chatas has precedence because it atones!

Answer: It refers to a regular Chatas.

Observation: This is unlike the question above (of Dam Chatas and Eimurei Olah), which discusses what itself is Mechaper and Kalil;

Here we discuss what comes to due to Kalil and Mechaper (Dam Olah is from a Korban that is Kalil. Eimurei Chatas are from a Korban that is Kalil.)

Possibility #1: Between Dam Asham and limbs of Olah, Dam Asham has precedence, because Asham atones like Chatas.

Possibility #2: Obviously limbs of Olah have precedence over Dam Asham, because they are Kalil;

This is unlike limbs of Olah and Dam Chatas. Dam Chatas is more important, for it is put on four Keranos.

Explanation: You are forced to say that it comes to exclude Olah, for if Olah has precedence over Asham, it should teach Olah [has precedence], and [we would know that all the more so Chatas, for Dam Chatas has precedence over Dam Olah!

Question: Why don't we bring a support from the Beraisa above (26a), which teaches that if Kodshim Kalim quivered [after Shechitah] and left the Azarah, it is Pasul?

We said about this "this teaches that meat of Kodshim Kalim that left [the Azarah] before Zerikah is Pasul", and answer that perhaps it refers to [Eimurim, i.e.] the tail, Yoseres ha'Kaved and the two kidneys.

Observation: They could have argued about Eimurim to teach Ko'ach d'Hetera (the extremity of the lenient opinion. R. Yochanan is Machshir even Eimurim.)