Why does it say "Zachar l'Olam Briso"?
Radak: This is like it says "Asher Karas Es Avraham" (verse 9) - that Bris He remembers for Avraham's seed forever. He gave the land to his seed after four generations. This is what He commanded. The land is always of Yisrael, even when they are exiled from it; they will return to it.
Malbim: The Bris with the Avos does not depend on people. "L'Olam" refers to time that is not divided.
What is the meaning of "Davar Tzivah l'Elef Dor"?
Rashi #1: The Torah, which He commanded to inform them in the world after 1000 generations, and He saw that the world does not exist without Torah, and He removed 974 (and gave it after only 26).
Rashi #2: He remembered for Yisrael His Bris that He commanded, and promised to guard it for them for 1000 generations - "Shomer ha'Bris veha'Chesed l'Ohavav ul'Shomerei Mitzvosav l'Elef Dor" (Devarim 7:9).
Radak: He decreed. Like He told Avraham, so He fulfilled to his seed. Radak (Divrei ha'Yamim I, 16:15) - this is like "Hashem Lo Tzivah" (Eichah 3:37). What He decreed Bein ha'Besarim, to give to Eretz Kena'an to their children, will be for 1000 generations.
Radak citing Shocher Tov: We expound l'Aluf b'Dor, i.e. Avraham Avinu; Elef is like 'Taku'a Alfa l'Shemen' (Menachos 8:3; it is best).
Malbim: What he commanded to people, is for generations - a generation comes and goes. The coming verses explain the Bris and command.
Why does the verse switch from "l'Olam" to "l'Elef Dor"?
Radak (Tehilim 105:8): There is no difference ("l'Elef Dor" is not precise).
Radak (Divrei ha'Yamim I, 16:8): The Bris He remembers for Avraham's seed forever. The promise to Avraham [to give the land to his children] was for 1000 generations.
