What does this Mizmor discuss?
Radak: It is about Bnei Galus. Every Chacham and Chasid praises and thanks Kel for the good that He does with him in Galus, and hopes for Ge'ulah.
Malbim: It discusses Hashem's conduct with man's spiritual Nefesh - He plans how man will not be cast off.
Why does it say "Barchi Nafshi Es Hashem"?
Malbim: The spiritual Nefesh, which is Bas Elokim, and a part of Hashem, blesses Hashem for the Chasidim that He does with it.
What is the significance of the five times that it says "Barchi Nafshi" in this Mizmor (verses 1, 2, 22) and the next (verses 1, 35)?
Radak, citing Brachos 10a #1: They were said for Hashem and the Neshamah. Just like Hashem fills the world, the Neshamah fills the body. Just like Hashem sees and is not seen, also the Neshamah. Just like Hashem sustains the whole world, the Neshamah sustains the body. Just like Hashem is Tahor, also the Neshamah. Just like Hashem dwells in a hidden place, also the Neshamah. Since the Neshamah has these five attributes, it should praise Hashem, who has them!
Rashi, from Brachos 10a #2: They hint to five periods for which David sang Shirah. Refer to 103:1:4:1, 103:2:2:1, 103:22:3:1, 104:1:2:1, 104:35:.3:1.
Radak citing Shocher Tov: They correspond to the five Chumashim.
What do we learn from "v'Chol Keravai Es Shem Kodsho"?
Rashi, from Brachos 10a: David sang Shirah for being in the womb.
Radak #1: Corresponding to the intellectual Nefesh, it says that all my innards should bless Hashem. "Keravai" are the kidneys and heart, which are internal.
Radak #2: "Keravai" refers to the body. It is a metaphor, like "Kol Atzmosai Tomarnah Hashem Mi Chamocha" (35:10). Ibn Ezra says that Shem ha'Etzem (Havayah), which is honored, is mentioned with the Nefesh, which is the Kavod of the body. Without it, the body is not important at all. Shem Kodsho is mentioned with the body; His name is not explicitly mentioned. 1
Radak citing Shocher Tov: This refers to 10 matters in man - the windpipe is for voice; the esophagus is for food; the liver is for anger; the lung is Lishtos, i.e. it draws [vapors] from liquids; the gall bladder is for envy; the stomach is for sleep; the stomach is for grinding; the spleen is for laughter; the kidneys counsel, and the heart finalizes. Therefore, David said "Odecha Al Ki Nora'os Niflesi" (139:14).
Malbim: Keravai is the body, which is a garment for the Nefesh. It blesses "Shem Kodsho", for it does not understand Hashem Himself, like the spiritual Nefesh does. Rather, it is like one who hears His name from afar, and blesses what it heard from afar.
Radak: There is no need to say so. Verses often repeat the matter in different words! "Kol Atzmosai Tomarnah Hashem" mentions Shem ha'Etzem with the body!