What does this Mizmor discuss?
Radak (2): The previous Mizmor discusses the Avos, and what Hashem did with Yisrael in Egypt. This Mizmor discusses what He did with them after they left Egypt, as long as they were in the Midbar and after they entered the land.
Malbim: It is a continuation of the previous Mizmor 1 . It discusses how Hashem guarded the Bris, took them out of Egypt and gave to them the land. It skips other miracles that He did for them after Yetzi'as Mitzrayim, e.g. Keri'as Yam Suf and splitting the Yarden.
Malbim (105:45, Divrei ha'Yamim I, 16:34): The previous Mizmor discusses the Chasadim that Hashem did with Yisrael when they left Egypt and in the Midbar. This Mizmor discusses how they rebelled against Him, their enemies ruled over them, and afterwards they were taken captive. It ends with a request to gather them from their captivity.
'Rashi' (Divrei ha'Yamim I, 16:34): Mizmorim 105 and 106 are one big Mizmor. Since it was big, it was divided into two. Also Iyov, when he needed to answer at length, he divided it into two, and it says "va'Yosef Iyov Se'es Meshalo" (Iyov 27:1, 29:1). Due to David's pining Simchah, he could not elaborate and needed to divide it into two. Also lamentation one cannot elaborate, and must divide into two.
Does thanking Hashem depend on "Ki l'Olam Chasdo"?
Malbim: They need to thank Hashem, for the great Chesed that He began to do for them, He did also after they sinned - "va'Yizkor Lahem Briso va'Yinachem k'Rov Chasadav." Hashem is good for His nation and His Chesed is forever, just they did not recognize His Chasadim and angered Him in every generation - "Lecha Hashem ha'Tzedakah v'Lanu Boshes ha'Panim" (Daniel 9:7).
