What is "ba'Eis ha'Hi" referring to? Why does the Torah insert the choosing of the Tribe of Levi here?
Rashi and Rashbam: It is referring to 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 B'nei Ya'akan, because there too, 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 Golden Calf. 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.
Bearing in mind that ythe tribe of Levi were chosen only after the census in Iyar of the second year
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 part of the Pasuk refers specifically to the Kohanim
Rashi in Zevachim, 26a also learns from this Pasuk that the Shechitah of Kodshim Kalim and the Kabalas ha'Dam (since they are included in 'Sheirus') must be performed in the Azarah.
What are the connotations of "Levarech bi'Shemo"?
Rashi (in 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.
Why does the Torah compare Avodah to B'rachah?
Refer to Bamidbar 6:23:151:1.