What was the Me'il?
See Oznayim la'Torah who explains why, according to the commentaries that the Me'il had four corners, it is nevertheless Patur from Tzitzis.
Why does the Torah refer to the Me'il as "Me'il ha'Eifod"?
Rashi: Because the Eifod covered it, and served as a belt to tie it.
Rashbam: Because the Eifod is worn on top of it. 1
See also Oznayim la'Torah.
What are the connotations of "K'lil Techeiles"?
Rashi #1, Rashbam and Targum Onkelos: It means 'completely of Techeiles'. 1
Rashi #2 and Targum Yonasan: It means 'twined threads' - and the minimum of 'twined' is two 2 - Rashi).
Menachos, 42b: It disqualifies any dye that was used for anything else - even for testing. 3
Rashbam: This is because i could be seen beneath the Choshen and the Eifod which the Kohen Gadol wore 'le'Ziakron' - and Techeiles too, serves as a Zikaron of the Kisei ha'Kavod, as the Gemara explains in Menachos, 73b - in connection with Tzitzis. See also K'li Yakar.
See Menachos (Ibid.), which also describes how the dye was prepared.
How thick were the threads of the Me'il?
