Why did David say that the Magid thought that he is a Mevaser?
Malbim: A Magid tells things that the listener has no benefit from them. Sometimes it is what he heard from others. A Mevaser tells things that the listener has benefit from them. Usually it applies to good tidings, what he saw himself. Sha'ul's death was Hagadah for David, for he did not think to get any benefit from it. 1 All the more so it was not good tidings for him!
Even if David did not plan to assert kingship over all of Yisrael, David benefited - he no longer needed to fear and flee from Sha'ul! (PF)
Why did David not say that the Magid said that he killed Sha'ul?
Malbim: David did not believe him. He thought that he said so, hoping to get reward.
Did David himself hold him and kill him?
Radak: Since he commanded a youth to kill him, it is as if he killed him. Perhaps David held him when the youth killed him.
Why did David kill him?
Malbim: It is because he was happy that Sha'ul died. 1
What is the meaning of "Lesisi Lo Besorah"?
Rashi, from Targum Yonasan: He thought that I would be happy to hear, and reward him for the tidings.
