1)
How could Moshe say "Ani Hashem Elokeichem"?
1.
Ramban: When Moshe left the presence of Hashem without the mask 1 and told Yisrael what Hashem had commanded him, it was self-understood that he was merely transmitting Hashem's words. 2
1
See the end of Ki Sisa.
2
And it was unnecessary to add "Koh Amar Hashem". Indeed, we find this format throughout Seifer Devarim - See for example the second Parshah of the Sh'ma (Devarim 13:15), where it was not Moshe, but Hashem, who sends the rain and causes the vegetation to grow (Ramban).