Why is it written Yinasen, and we pronounce it Yutan?
Radak: The writing is Nif'al. Even if you do not give them, Hashem will give (punish them for us). The pronunciation is Pa'al - you should give them.
Why did they request seven?
Yerushalmi Sanhedrin 6:7: Sha'ul killed seven Giv'onim when he killed Kohanei Nov.
Radak (1): There were seven survivors from Beis Sha'ul of those who killed the Giv'onim. Refer to 21:7:2:3.
Malbim: There were only seven survivors from Beis Sha'ul, excluding from Yehonason. They knew that Yehonason did not consent to eradicate Nov, for he had a Bris with David.
Why did they say "v'Hoka'anum la'Shem"?
Rashi: We will hang them for the sake of Hashem, to publicize His judgment (Radak - that He wants to avenge what was done to us).
Why did they want to hang them?
Radak: This way, all Yisrael will see their vengeance, and be careful not to harm Giv'onim again. Malbim - they will learn from a Kal v'Chomer. If so was done to the king's sons for harming us, all the more so others [who harm us will be punished harshly]! They did not seek vengeance, just to fix the matter so they will not be pursued any more. 1
Why did they want to hang them in Giv'as Sha'ul?
Malbim: Bnei Binyamin and Sha'ul's family live there; they are drawn after his mindset. When they see the men hung in Giv'as Sha'ul, they will fear and not sin b'Mezid again.
Who called Sha'ul "Bechir Hashem"?
Rashi citing Brachos 12b: A Bas Kol (voice from Heaven) said so. Radak - i.e. his sins were pardoned.
Radak: They said it; Hashem chose him to be king.
Children do not die for the sins of their fathers (Devarim 24:16))!
Radak (1): It is better to uproot a Parshah in the Torah than to have Chilul Hashem. I.e. the Nesi'im had sworn not to kill them [and they killed them]! Also refer to 21:6:8:1.
Radak (1) #2: Beis Din does not kill children for the sins of their fathers This punishment was bi'Ydei Shamayim.
Why did he say "I will give"?
Malbim (from Bamidbar Rabah 8:4): This was unlike Torah law. The Torah says that we do not kill two people the same day 1 , and not children for the sins of their fathers, and to hang the bodies on the tree [after the day of death]. Only a king may do so 2 , like the Rambam says (Hilchos Melachim 3:10).