Why did Og live so long?
Targum Yonasan: When Og saw that Avraham and Sarah could not have children, he would mock them, comparing them to trees that are planted beside pools of water but which does not produce fruit. Consequently, Hashem let him live to see how Avraham's descendents had multiplied and then to fall into their hands. 1
Why did Hashem need to instruct Moshe not to be afraid of Og?
Ramban #2: Because, since Moshe did not plan to capture the lands of Sichon and Og, 3 he was about to veer away from Og as they had done regarding Edom; so Hashem instructed him not to fear but to go ahead and take up the challenge.
Ramban #3 (citing the Midrash): Because Moshe was afraid that Yisrael had somehow sinned during the war with Sichon. 4
Rashi: In that he informed Avraham that Lot was captured (See Bereishis, 14:13), as a result of which Avraham fought with the four kings and recaptured him. Ramban: Because otherwise, it is inconceivable that Moshe - who warned Yisrael not to be afraid of the Cana'anim (See Devarim 31:6 and Devarim, 1:29-30), should be afraid of flesh and blood.
See Sifsei Chachamim.