Seeing as "Kelayos" automatically implies two, why does the Torah add the word "Sh'tei"?
Bechoros, 39a: To render Pasul an animal that is found to have one or three kidneys.
What are the implications of "ve'es ha'Cheilev ... asher al ha'Kesalim"?
What is the "Yoseres al ha'Kaveid"?
Rashi, Targum Onkelos and Targum Yonasan: It is the diaphragm (a wall of fat that divides between the limbs that govern one's breathing and those that deal with the food). 1
Rambam and Rashbam: It is the lobe of the liver' (and is called "Yoseres ha'Kaveid" because it grows on the liver and enlarges it - Rashbam). 2
Does the Kohen take the Yoseres together with the liver or a bit of liver together with the Yoseres?
Sifra: Based on the Pasuk in Shemini, 9:10, in connection with the calf of the Chatas on the eighth day of the Milu'im "ve'es ha'Yoseres min ha'Kaveid", it is clear that he takes a bit of the liver together with the Yoseres. 1
See Torah Temimah, note 26, who elaborates.
Where exactly is the Cheilev that is described in this Pasuk?
Rashi: When the animal is alive, the Cheilev that is on the kidneys is on top of the flanks, which in turn, are underneath the loins. It is synonymous with the white that can be seen on top of the flanks, whereas the Cheilev on the lower part of the flanks is covered by the flesh.
What does the last part of the Pasuk mean? What does one remove and what does one not remove?
Rashi: It means that the Kohen removes the Yoseres together with a bit of the liver, but leaves intact the bulk of the liver and the kidneys.
Why does the Torah write "Yesirenah" (singular) and not 'Yesireim' (plural)?
Sifra: To teach us that each of the above items is independent. Consequently, if (after the blood has been sprinkled ? Ha'Torah ve'ha'Mitzvah) the kidneys, the Yoseres or one kidney go missing, the Kohen removes whatever remains and brings it on the Mizbe'ach.
