Radak #1: This refers to reward in the world to come. Even though man's body perishes, Chesed Hashem does not perish. It is always on those who fear Him, i.e. on their Neshamos, without ceasing. It is called Chesed because it is for Yera'av, which is a lower level than Ohavav. The good that He does with them is always Chesed; it is more good than they deserve. Just like He guards the good for them for the world to come, He guards it for them in this world, for their children after them.

Radak #2: This refers to this world. After a person dies, Chesed Hashem pays reward of his good deeds to his children, forever.

Malbim: Even though the body dies and does not last long, the Nefesh remains forever; Chesed Hashem is forever on those who fear Him. After he departs from this world, Chesed Hashem accompanies him to the second world, which is eternal. There it will live in eternal bliss.

Radak: It is His straightness. He rewards their children with love for them, according to their deeds. This is one of His 13 Midos.

Radak citing Shocher Tov, Malbim: It is the person's virtue.

Radak #1: No, it is for 1,000 generations - "l'Ohavav ul'Shomerei Mitzvosav l'Elef Dor" (Devarim 7:9). Even 1,000 is not precise, for it says 2,000 ¹ .

Radak #2: No, it is forever; this repeats the beginning of the verse.

Radak citing Shocher Tov: Yes. Chesed Hashem is forever, but Tzedakah is until three generations - his grandchildren. A Chasid, who does more than he is commanded, Hashem guards his Chesed for his children after him, forever. If he is only a Tzadik, who does what he is commanded, Hashem guards his Tzedakah to his children after him until the third generation.