Who waved the above listed sections of the Korban Milu'im?
Rashi: Moshe (the Kohen) placed his hands underneath those of Aharon and his sons (the owners), and they waved them together.
What procedure did the Tenufah and the Terumah (that verse 27 mentions) follow?
Rashi: They waved them in all four directions (Tenufah), 1 and up and down (Terumah).
See Sifsei Chachamim.
What was the purpose of the Tenufah and the Terumah?
Rashi: The Tenufah was to acknowledge that all four directions belong to Hashem - thereby preventing all forms of punishment that is caused by harmful winds; and the Terumah to acknowledge that Heaven and earth belong to Hashem - thereby preventing harmful dews.