How will Hashem reign forever?
Rashi: He will sustain His kingship via guarding His children.
Radak: He will reign Al ha'Olam (on the entire world) - "v'Hayah Hashem l'Melech Al Kol ha'Aretz" (Zecharyah 14:9).
Why does it say "Elokayich Tziyon"?
Radak: From there Hora'ah (instruction) goes out to the entire world.
Malbim: This refers to Hashem's particular connection with Tziyon, and the Hashgachah Pratis to do wonders there.
Why does it say "l'Olam" and "l'Dor va'Dor"?
Malbim: "L'Olam" refers to a constant period of time without divisions. This applies to Shem Havayah - general Hashgachah on all the creations according to natural orders and the Ma'arachah. This is fixed conduct that does not change. "L'Dor va'Dor" is periods of time with divisions. Miraculous conduct is not fixed forever; it changes according to the need of the generation, their preparation and merits.
