Why did he say "Baruch Hashem"?
Rashi: When I recover, I will say so.
Radak: (In the previous verses, the Choleh spoke.) Now the author speaks. He thanks Hashem for completing the Sefer 1 ; so is the custom. (Tehilim is divided into five Seforim; this completes the first.) He thanks Hashem at the end of each, and has 13 praises at the end of the last Sefer.
Malbim: After this are the Mizmorim of Bnei Korach.
Why did he say "me'ha'Olam v'Ad ha'Olam"?
Radak: From the first time until the last time - i.e. all days.
Malbim: All the Brachos and praises in this Sefer should be in the mouths of Yisrael forever, for all generations.
Why does it say "Amen v'Amen"?
Radak: Kiyum (affirmation and persistence) and Kiyum. This is like one who answers Amen after a Brachah to be Mekayem it. Also "v'Ne'eman Beisecha" (Shmuel II, 7:16) is an expression of Kiyum.