What are the implcations of "be'Vo'am el Ohel Mo'ed"?
Zevachim, 26a: It implies that, when performing the Avodah, the Kohen must be completely inside the Azarah, and that, even if just some of his hair is protruding outside, his Avodah is Pasul.
What is the practical difference between "coming to the Ohel Mo'ed" and "approaching the Mizbe'ach", for both of which a Kohen without the Bigdei Kehunah is Chayav Misah.
Why does the Torah add the word "ba'Kodesh"?
Zevachim, 119b: To teach us that Bigdei Kehunah are not required on a Bamah Ketanah. 1
On which even a Zar is allowed to serve. See Torah Temimah.
What are the implications of "ve'Lo Yis'u Avon va'Meisu"? What is it referring to?
Rashi and Ramban #1 (according to the simple P'shat): It teaches us that a Kohen Hedyot who performs the Avodah without the four specified Begadim or the Kohen Gadol without his eight Begadim is Chayav Misah.
Ramban #2 (citing Zevachim 17b): It teaches us that a Kohen Hedyot or a Kohen Gadol who serves without the pants is Chayav Misah. 1
See Ramban DH 've'Lamadnu" for the source of Chiyuv Misah regarding the other Begadim.
What kind of Misah did the Kohen who transgressed receive?
Targum Yonasan: Refer to 28:35:2:4 and note.
Why does the Torah add "ve'Lo Yis''u Avon Vameisu", which it did not do earlier in connection with a Zar and with the Me'il)?
Oznayim la'Torah: Because, in addition to serving without the Michnasayim (according to the Ramban), he also entered the Mishkan improperly dressed - thereby transgressing the laws of Tzeniyus. 1
Oznayin la'Torah: Something that the Torah warned against above at the end of Yisro.
What are the connotations of "Chukas Olam"?
Rashi: Wherever this term is used, it always means that the Mitzvah under discussion together with its details applies at all times.
QUESTIONS ON RASHI
Rashi writes that the current Pasuk teaches us that a Kohen who serves without his four Begadim is Chayav Misah. But we already know from from "v'Chagarta..." in 29:9) that a Kohen without the Begadim is like a Zar (Zevachim 17b), and a Zar who serves is Chayav Misah?
Riva #1, Da'as Zekenim and Hadar Zekenim: "ve'Chagarta..." does not apply to the pants; The current Pasuk therefore teaches us that a Kohen is Chayav Misah if he serves without them. 1
Riva #2: The current Pasuk obligates Misah for serving without the four Begadim, whereas "ve'Chagarta..." teaches us that a Kohen Gadol is like a Zar if he does not wear all eight Begadim.
Tosfos (in Yoma 5b DH 'Lehavi'): Some say that the current Pasuk obligates Misah for one who entered the Mishkan without pants, even if he is not serving, and the Tosefta in Keilim 1:6 supports this. 2
Moshav Zekenim (in 29:9): The current Pasuk obligates only if oneenters the Ohel ha'Mes or approaches the Mizbe'ach, whereas "ve'Chagarta..." obligates Misah for Avodos anywhere in the Chatzer ha'Mishkan - such as when permorming the Kabalas ha'Dam.
Tosfos (in Yoma 5b DH 'Lehavi'): This does not concur wih the opinion that the 'Vav' in "ve'Zeh ha'Davar" - 29:1 comes to add to the previous Parshah, and that "ve'Chagarta..." therefore applies even to the pants.
Tosfos (Sanhedrin 83b DH 'Ein'): This is wrong. All opinions exempt from Misah for entering without serving, like I proved above - in 83a DH 've'Lo'. Tosfos there proved this from a Gemara, but concedes that it concurs with the Tosefta - PF)
