What is "Aliyas ha'Sha'ar"?
Radak: There was a room on top of the gate. The lookout stood on top of the roof of that room, like it says above (18:24) "El Gag ha'Sha'ar."
Why did he say "Bni" so many times?
Rashi citing Sotah 10b: He said so eight times (including three times in verse 5). Seven times were to save him from the seven chambers of Gehinom, and one was to bring him to the world to come. 1 Malbim - "va'Ya'al" is Po'el Yotzei; David raised him, like "Morid She'ol va'Ya'al" (Shmuel I, 2:6).
Radak: People who sigh often repeat their words, e.g. "Me'ai Me'ai Ochilah" (Yirmeyah 4:19).
Malbim: (a) Even though he rebelled, David was pained, for Avshalom did not want to kill David, only to rule after him. You acted like Bni, and not like a cruel stranger who wants to kill me. Bni Bni - you were my primary son, proper to rule after me. 2 (b) The rebellion was caused via David's sin 3 , like the Navi told him.
Sotah 10b: Some say that the eighth was to get his head to rejoin his body.
What is the source to say so? Kil'av was older than him (refer to 14:15:1:2*), and Amnon was the oldest, just Avshalom killed him. Should Avshalom merit kingship via murder? If Amnon was disqualified due to his sin, also Avshalom should be! Why was he more proper than Shlomo? Hashem chose kings from Bas Sheva's seed, and "He called [Shlomo] Yedidyah", "and Hashem loved him" (12:24-25)! David swore to her that her son will be king after David (Melachim I, 1:13)! (PF)
Hashem "punishes children for their parents' sin" (Shemos 20:5) only when also the children sin (Brachos 7a)! Hashem did not decree that any particular son will rebel. Had Avshalom merited, surely Hashem would not have brought this terrible matter through him! (PF)
Why would David prefer that he died, and not Avshalom?
Malbim: Avshalom was a Tzadik; he was punished due to his father. 1 This is why he said first 'Avshalom'.
Refer to 19:1:2:3**.
