What did David promise to the one who will strike them?
Rashi: The verses here did not say. In Divrei ha'Yamim (1:11:6), it explains that he will be the head general; (Radak - Yo'av did so). Also "Kol Horeg Kayin" (Bereishis 4:15) does not say what will be done to him; it is understood that this condemns doing so.
Malbim: He merely said that one who will strike them must go in this order - Yevusi, Tzinor, Pischim and Ivrim. (Refer to 5:8:4:1.)
What is the meaning of "v'Yiga ba'Tzinor"?
Rashi citing Targum Yonasan: He will begin to capture the city.
Rashi: The Tzinor was the top of the tower. Radak citing a Midrash: They could not conquer the Yevusi without reaching it. They brought a Brush (pine) tree and bent it. [When they let it spring back,] Yo'av jumped onto the top of the wall 1 . They wanted to kill him; he fought valiantly, and Giborei Yisrael helped him.
Radak: He will strike the strong place.
R. Yeshayah: He will [open, remove or break] the lock used to lock the gate.
Malbim: He will [disrupt] the flow of water that causes the images to move the iron rods [which inhibit entering through the gate].
Radak citing Shochar Tov 18: Yo'av stood on David's head, hung on the tree and jumped onto the wall. Hashem lowered the wall, and David was able to pass over it. Tehilim 141:5, 18 hints to this. (Surely, he stood on David's head because David was tallest - refer to Shmuel 1 17:38:1:1; from another's head, he could not reach the tree - .PF)
What is the meaning of "v'Es ha'Pischim v'Es ha'Ivrim"?
Rashi: He will strike also them.
R. Yeshayah: He will remove them.
Why are the Pischim mentioned before the Ivrim? In verse 6, it mentions the Ivrim first!
Malbim: After David conquered the Metzudah on the other side of Yerushalayim, he requested someone to continue from that direction and strike the Pischim and Ivrim. Verse 6 discusses one who comes to enter via the gate; he encounters the Ivrim first.
Why are they called "Senu'ei Nefesh David"?
Radak (6): He hates hearing and seeing 1 idolatry.
Radak: They disgraced David through them, saying that they will stop him from conquering the Metzudah.
Presumably, the text should say so, like in Pirkei d'R. Eliezer 35, and not 'umi'La'avod' (PF).
What is the meaning of "Al Ken Yomru Iver u'Fise'ach
Rashi: [David hated them,] for they said that as long as the Pischim and Ivrim are here, David cannot come.
Radak: From when David conquered it, they said that a blind or lame person may not enter Metzudas Tziyon, to disgrace the Pischim and Ivrim that used to be there, and as a remembrance of how David conquered it.
Malbim: Because they say that David may not enter, it is proper to strike them.