Why did he call to "Hashem Tzevakos"?
Malbim: Until now, David was Sar Tzevakos Yisrael to fight against Pelishtim. Now that David must flee, it is upon Hashem to be Sar Tzevakos 1 and fight their wars.
Avner was Sar Tzeva before David fought Galyus, and also after (Shmuel I, 14:50, 26:5)! If David means that he was the means of their victories, Yehonason was still around; also he overcame Pelishtim (Shmuel I, 14:45)! This requires investigation (PF)
Why did he say "Hakitzah"?
Radak: Now, they chase him without any sin, and no judges of Yisrael tell Sha'ul that he does improperly; rather, they flatter him. Since Hashem delays anger towards them, it is as if He sleeps.
Why did he ask Hashem to be Poked all Goyim?
Rashi: He asks Hashem to judge the Resha'im like all nations, and not have mercy on them.
Radak: I will not see the generation righteous, until You refine the world (both Goyim and Yisrael) like a smith refines silver, and the Resha'im will be eradicated.
Malbim: Hashem should amass forces against all the nations that come to fight Yisrael.
What is the meaning of "Al Tachon Kol Bogdei Aven"?
Radak: Hashem will no longer delay anger against the Resha'im - "v'Shavtem u'R'isim Bein Tzadik l'Rasha Bein Oved Elokim la'Asher Lo Avado" (Mal'achi 3:18).
Malbim: Even though I ask You to save Yisrael, do not have grace on Sha'ul and his men who are treacherous to kill me; they should die in the war.