1)
How will the Minchah prove that Hashem Himself speaks with him?
1.
Malbim (17): An angel would not be able to accept a Korban 1 , for "Zove'ach la'Elohim Yacharam Bilti la'Shem Levado" (Shemos 22:19). This is why the angel told Mano'ach "Im Ta'aseh Olah la'Shem Ta'alenah" (13:16).
1
If. Gid'on offers a Korban to Hashem, what is the difference whether the one with whom he spoke was an angel or Hashem? Malbim understands that "Lefanecha" means that I offer the Korban to You, the One who speaks to me. (PF)
2)
How could he offer Korbanos? The Mishkan was in Shilo, and Bamos were forbidden!