What is the grammatical form of "Habet" and "u'R'e"?
Radak: Both of them are Makor (like an infinitive); they are not commands. Refer to 142:5:2:2.
Why does it say "Habet Yamin"?
Radak: The verse mentioned only right, and not left. Many verses are abbreviated; from one, the other is understood. E.g. "Imo ha'Reuveni veha'Gadi Lakchu Nachalasam" (Yehoshua 13:8), i.e. with Chetzi Menasheh. The half of Menasheh with the nine and a half tribes was mentioned, so it is understood that "Imo" means with the other half, as if it was mentioned.
Malbim: If I will go south, no one will recognize me.
Why does it say "v'Ein Li Makir"?
Rashi: None of Sha'ul's servants protest against him.
Radak: When I look right and left, there is no one to recognize me and have mercy on me and my forced wandering.
Why did he say "Avad Manos Mimeni"?
Radak: When I plan to go to a place, and there Sha'ul will not know and not pursue me there, there is no such place. Anywhere I go, he will seek me.
Malbim: If I will flee backwards, to the west, escape is lost from me, for the enemies are in back of me. The verse depicts that on one side, north, there is the mountain with the cave that blocks him from going there, and enemies are on the other three sides.
What is the meaning of "Ein Doresh l'Nafshi"?
Radak: Of all my redeemers and relatives, no one seeks [to save] my Nefesh, which Sha'ul wants to take. I will not find a redeemer from the king, if You will not redeem me.
Rashi: I cannot hope for help from a lover or savior.