What is "ba'Eis ha'Hi" referring to? Why does it insert the choosing of the Tribe of Levi here?
Rashi: It is after the episode of the Golden Calf 1 . Levi did not go astray then, and that is why Hashem chose them, as the Pasuk goes on to explain. It is mentioned here, following the episode of Benei Ya'akan, for also there, the tribe of Levi did not go astray.
Ramban: It refers to the same time as "ba'Eis ha'Hi" in Pasuk 1 - after Hashem instructed Moshe to carve out a second set of Luchos, when He made up with K'lal Yisrael and commanded them to build the Mishkan, that is when the Levi'im were chosen. 2
Seforno: It is following the sin of the Eigel ha'Zahav. Moshe was pointing out that Hashem chose the Tribe of Levi to serve Him and the rest of Yisrael remained unworthy of doing so. It is a sign that he only achieved with his Tefilah that Hashem did not destroy them, but not a complete pardon.
Rashi writes that Shevet Levi was choen due to the episode of the Golden Calf . They were chosen only after the census in Iyar of the second year (Bamidbar 1:1)!
Ramban #2: Refer to 10:8:1:2.
What has "La'amod Lifnei Hashem Leshorso u'Levarech bi'Shemo" to do with the Levi'im?
Rashi: This Pasuk is talking about the entire Tribe of Levi, including the Kohanim. 1
Rashi in Zevachim, 26a also learns from this Pasuk that the Shechitah of Kodshim Kalim and the Kabalas ha'Dam must be performed in the Azarah.
What are the connotations of "Levarech bi'Shemo"?
Rashi (Eruvin, 18b): It means to bless the people with the Name of Hashem - the way it is written. 1
Which is what the Kohanim did in the Beis ha'Mikdash.
Why does the Torah add the words "Ad ha'Yom ha'Zeh"?
Ramban: Which also explains why, in Pasuk 6, the Torah mentioned the appointment of Elazar after Aharon's death. ("Ad ha'Yom ha'Zeh" does not refer to Leviyim carrying the Aron, for this Avodah was basically only in the Midbar, and does not apply at all after the Beis ha'Mikdash was built.
What do we learn from the Hekesh of Avodah to Brachah?
Refer to Bamidbar 6:23:151:1.