When was Moshe instructed to perform this task and when did he carry it out?
Rashi: Although he was issued with the instructions now, he will only carry them out later, after the construction of the Mishkan was completed. 1
See Sifsei Chachamim. Moshav Zekenim: The Torah writes in Tzav Vayikra, 8:12 that Moshe anointed Aharon to be Mekadesh him, but it was not completed until he sprinkled on him and his sons and their garments with the oil and blood of the Milu'im - Ibid. Pasuk 30.
Having stated "Aharon and his sons", why did Hashem need to mention them all by name?
Ramban: To teach that they all required individual anointing, and should not rely on the fact that Aharon was anointed and they were his sons and to preclude (Pinchas and any other grandchildred who were already born.
Refer to Bamidbar, 25:13:2:1.
What are the connotaions of "Lechahano Li"?
Da'as Zekenim: Whenever the Torah uses the word "Li", it means forever. 1
Ibn Ezra, Targum Onkelos and Targum Yonasan: It means 'to serve as priests for Me' (because the 'Vav' in "Lechahano" is superfluous - Ibn Ezra). 2
Da'as Zekenim: For example "Ki Li Kol Bechor", "Ki Li B'nei Yisrael", "Ki Li ha'Aretz."
Ibn Ezra: Like we find in Tehilim, 104:11 and in Balak, 24:3. Refer also to 28:4:8:1.