Gen 17:1-5

Questions

Who is the Almighty God speaking to Abraham here (v.1)?
How does the command to be "perfect" (v.1) in the Abrahamic tradition compare to the concept of perfection (being without spot) in the Mosaic tradition? Are they different? Can we see the Lord repeating this command during his earthly ministry as a restoration of a lost principle?

The title translated as Almighty God here is the Hebrew El Shaddai--Shaddai being used most frequently as a name for God in the book of Job (31 references).
The Hebrew term "tamiym" is translated here as "perfect", but is translated as "without blemish" almost 40 times in Numbers and Leviticus. Some modern scholars translate the word as "blameless."
The word translated as God in verse 3 is the Hebrew Elohim.

Many biblical scholars consider this story to be part of the E (for Elohim) tradition of Northern Israel, where God is consistently referred to as Elohim. Later, when the J (for Jehovah) traditions are brought together with these stories, the writers tried to equate Elohim with Jehovah (see Ex 6:3).
The title El Shaddai (Almighty God) appears only in writings that are thought to predate the Deuteronomistic reforms starting in the time of King Josiah (see list here). It is a curious term, as shad is Hebrew for women's breasts, and may be related to the Hebrew shuwd (destruction). The use of this name for Elohim is usually either used in a context of either fertility or destruction (see especially its former connotation in connection with breasts in Gen 49:25).
The title Almighty also occurs 11 times in the Book of Mormon--which was written by the descendents of Lehi, who left Jerusalem before the Bible was fully re-edited by the Deuteronomist reformers. In the Doctrine and Covenants, the title is used 10 times, see especially D&C 20:21 where the title refers to God the Father, and D&C 20:24 where Christ is given Heavenly Father's "almighty" power.