What is the definition of an Eglas Bakar?
Targum Yoinasan: It is 'a calf' - a cow in its first year.
Why is the nearest town obligated to bring the calf?
Ramban #1 (in Pasuk 4, citing the Ibn Ezra): Because had the inhabitants of that town not performed a similar sin, a person would not have been killed in their close proximity.
Ramban #2 (in Pasuk 4, citing the Moreh Nevuchim) and Targum Yonasan: Because the murderer is probably a resident of their town. 1
What if the corpse is equidistant from two towns?
Why does the Torah write "Ziknei ha'Ir ha'Hi" and not simply 'Zekeinehah"?
Sotah 45b: To preclude a town that does not have a Beis-Din, which is not included even in the measuring in the event that it is the nearest town, and they only measure to the towns which do have a Beis-Din. 1
See Torah Temimah, citing Sotah, 45b., and Note 22 - that this is not the Halachah. Refer also to 21:4:0.1:1.
What are the implications of "asher Lo Ubad bah"?
Pesachim, 26a: Since the Torah writes "Avad bah" (without a 'Vav'), 1 and we read it "Ubad" (as if it had a 'Vav') 2 , we conclude that it worked on its own it is not Pasuk unless the owner benefitted from it. Consequently, if the owner placed it in the stable to suckle from its mother together with other calves and it threshed the corn 3 or if a bird rested on it, it remains Kasher, whereas if the owner placed it in the stable 4 to suckle and to thresh or if if a male came on it, it becomes Pasul.
Sotah, 46a: "Bah" precludes a Kodshim animal, which does not become Pasul through Avodah. 5
What are the specifications of 'Meshichas Ol"?
Seeing as all kinds of Melachah render the calf Pasul, why does the Torah mention specifically drawing a yoke?