Was Sha'ul permitted to kill himself?
Radak: Yes. Even though it says "v'Ach Es Dimchem l'Nafshoseichem Edrosh", i.e. I will demand (punishment) if you kill yourselves, and similarly "mi'Yad Kol Chayah Edreshenu umi'Yad Ish Achiv", even so he did not sin, for he knew that his end is to die in war, for so Shmuel told him, and he saw that the archers found him and he could not escape. It was better than that he kill himself, and the Arelim will not make a mockery of him. Chazal (Bereishis Rabah 34:13) expounded, perhaps Ach Es Dimchem l'Nafshoseichem Edrosh includes the case of Sha'ul! "Ach" excludes this.
Did he die through falling on his sword?
Radak #1: No, he became close to death. This is like "b'Tzeis Nafshah Ki Mesah" (Bereishis 35:18). He did not die until the Amaleki killed him, like he himself told David (2:1:10).
Radak: Yes. The Amaleki lied; he already found him dead on his sword. He thought that he will find grace in David's eyes by saying that he killed him.
Malbim (4): No, he became only Goses (close to death). It says that he died for he was mortally wounded.
