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'
Rashbam: This is because i could be seen beneath the Choshen and the Eifod which the Kohen Gadol wore 'le'Ziakron'
How thick were the threads of the Me'il?