Why does it say "v'Samach Yado"?
Ramban, Moshav Zekenim: Really, Semichah is with both hands, like we find elsewhere 1 . The Torah writes "Yado" (singular) to preclude performing Semichah via a Shali'ach, even though normally, one's Shali'ach is like himself.
Targum Yonasan: Semichah is with the right hand, forcefully.
Why does the Torah write "al Rosh ha'Olah" rather than "al Rosho"?
Rashi: To incorporate an Olas Chovah and Olas Tzon in the Din of Semichah. 1
Riva: However, the Olah of the Tzibur, women or Nochrim do not need Semichah. All of them require Nesachim, even of a Nochri (Shekalim 7:6).
For what does an Olah atone?
Rashi (from Toras Kohanim): It atones for the transgression of an Asei and of a Lav ha'Nitak l'Asei 1 (a Lav that can be rectified by performing an Asei).
Ramban #2 (citing Vayikra Rabah 7:3), Moshav Zekenim (12:8 citing Yelamdenu) and Seforno (2): It atones for sinful thoughts. 2
Da'as Zekenim, Hadar Zekenim: If one was sure that he ate Shumen, and really it was Chelev, he did not forget anything; Olah atones for this.
Ramban: B'Meizid, for the Torah did not teach any other punishment or atonement for these. It does not mention Shogeg here, like it says about Chatas. When the Torah gave the punishment only for Mezid, we can say that there is no punishment for Shogeg. However, we cannot say that there is no punishment for Mezid!
What exactly, does "v'Nirtzah Lo" mean?
Ramban #1: Hashem will be pleased with his Korban and atone for him. 1
Ramban #2: His sin will be forgiven. 2
Rashi writes that Olah atones for an Asei and a Lav ha'Nitak l'Asei. If he did not repent, "Zevach Resha'im To'evah" (it is not accepted). If he repented, he was immediately pardoned (Yuma 86a)!
Zevachim 7b: The Olah is a gift. (It need not atone, for it is brought after Teshuvah.)
Moshav Zekenim, Riva: Really, he repented. He immediately gets a weak Kaparah; through an Olah, he gets a full Kaparah.
Rashi writes that Olah does not atone for Aveiros for which the punishment was taught. Se'ir ha'Mishtale'ach atones for all Aveiros, even those with punishments. We can say similarly about Olah! And elsewhere, we say that Olah atones for [sinful] thoughts, or that it is a gift after Teshuvah!
Moshav Zekenim: Se'ir ha'Mishtale'ach has a fixed time (Yom Kipur). We can say that he can be afflicted before this. One can offer Olah at any time. It is unreasonable for afflictions to come before he offers it. 1
One may bring Asham Taluy at any time, and one can be afflicted before he brings it! (PF)
Rashi writes that Olah atones for an Asei and a Lav ha'Nitak l'Asei. What is the case?
Moshav Zekenim: He was obligated in the Aseh; there is no punishment for not fulfilling it, just he stumbled through a lack of zealousness to fulfill it. If he transgressed a Lav and fulfilled the Aseh to which it is Nitak, he initially stumbled; an Olah atones for this.
Rashi writes that "Al Rosh ha'Olah" teaches about Semichah for Olas Tzon and Olas Chovah. We can learn both of these from "ka'Mishpat" (9:16), i.e. Olas Chovah is like Olas Nedavah, i.e. it requires Semichah (Beitzah 20a); this applies also to the lamb (Tzon)!
Moshav Zekenim (9:16): One might have thought that "ka'Mishpat" teaches Semichah only for the calf, for we find Semichah on cattle of Olas Nedavah. Due to "Al Rosh ha'Olah", we establish it also for the lamb.
Rashi writes that "Al Rosh ha'Olah" teaches about Semichah for Olas Chovah. Why don't we can learn this from "va'Yakrev Es Eil ha'Olah va'Yismechu
Moshav Zekenim (9:16) #1: "Ka'Mishpat" implies that this is the law; it was not a Hora'as Sha'ah.
Moshav Zekenim (9:16) #2: Korban Aharon is different. We can say that learn other Olos from it.