1. I would bet he's saying the equivalent of, "I am eating," which would mean A, he's has sat down and hasprepper and is planning to eat, so he is "eating" in a more general sense, and B, he's eating Akane up with his eyes.
2. Dunno. "Shoo" is used most for children and houseflies, "shoo them away," perhaps "phu-u-u" is a better sound for blowing on hot food.
Thanks for the translation!