1)
Who actually put the murderer to death
1.
Targum Yonasan: Either the Go'el ha'Dam (the next of kin of the victim) or Beis-Din
1
See Na'at Yonasan.
2)
Sotah 2a learns from "Lo Yakum Ed Echad b'Ish" (Devarim 19:15), that elsewhere, "Ed" is two witnesses. Why don't we learn from a Binyan Av, that everywhere it is one? Also, we could learn from our verse "v'Ed Echad Lo Ya'aneh", "Lo Yamus Al Pi Ed Echad" (Devarim 17:6) and "Lo Sa'aneh Ed Shaker" (Shemos 20:13)
1.
Refer to 5:13:153:1,2 and the note there.