"Makeh Nefesh" implies even a Nefel who is going to die and an eighth-month baby. Does this mean that one is Chayav Misah for killing a Nefel?
Sanhedrin, 84b: That is why the Torah writes in Mishpatim, Sh'mos, 21:12 "Makeh Ish va'Meis Mos Yumas", to preclude someone who kills a Nefel. 1
How is the murderer put to death?
Yerushalmi Sanhedrin, 6:3: We learn via a Gezeirah Shavah 'Nekimah' (Sh'mos, 21:20) 'Nekimah' (Vayikra, 26:25) 1 that a murderer is killed by the sword (Hereg) - irrespesctive of how he killed his victim.
Refer to Vayikra, 26:25:2:3 and note.
Who actually puts the murderer to death?
Targum Yonasan: Either the Go'el ha'Dam (the next of kin of the victim) or Beis-Din ? via two witnesses who are eligible to testify. 1
Having stated "Kol Makeh Nefesh L'fi Eidim (plural) Yirtzach es ha'Rotze'ach", why does the Torah need to insert "ve'Eid Echad Lo Ya'aneh ... "?
Sanhedrin, 33b: To teach us that one witness is not believed, irrespective of whether he comes to declare the accused innocent or guilty.
Sanhedrin, 34a #1: To teach us that the witnesses are not permitted to raise a point - even in favor of the accused. 1
Sanhedrin, 34a #2: To teach us that if one of the Talmidim wants to raise a point against the accused, he is not permitted to do so - "Echad Lo Ya'aneh be'Nefesh la'Mus". 2
The Gemara in Sotah, 2a learns from "Lo Yakum Eid Echad be'Ish" (Shoftim Devarim, 19:15), that elsewhere, "Eid" refers to two witnesses. Why don't we learn from a Binyan Av, that it always means one witness? Moreover, we could learn that it means one witness from the current Pasuk "ve'Eid Echad Lo Ya'aneh", from "Lo Yamus al-Pi Eid Echad" (Shoftim Devarim, 17:6) and from "Lo Sa'aneh Eid Shaker" (Yisro Sh'mos, 20:13) ? seeing as it is obvious that even one witness may not lie?
Refer to 5:13:153:1 & 2 and note.