What is the difference between "coming to the Ohel Mo'ed" and "approaching the Mizbe'ach" (bot of which render a Kohen without the Bigdei Kehunah Chayav Misah?
What are the implications of "ve'Lo Tis'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 are the connotations of "Chukas Olam"?
Rashi: It always means that the Mitzvah under discussion together with its details applies at all times.