1)
Why did he kill Adoniyahu through Benayahu, who was a Kohen (Divrei ha'Yamim I, 27:5)?
1.
Radak #1: Adoniyahu did not die when Benayahu first struck him. Benayahu pulled back [from contact with him] before he died.
2.
Radak #2: Even though a Kohen may not become Tamei Mes, for the sake of a Mitzvah it is permitted; the command of the king is a Mitzvah. And so a Kohen may fight a war of a Mitzvah and become Tamei; therefore, Shlomo made him the head general. (Also refer to Shmuel II, 23:20:4:1 and the note there.)
