My CAG, Chance (although, I'm her pet, not the other way around) always has fresh water (I use purified) and always has food available to eat. Sometimes she eats at random times, like a snack, just like we humans do. But she likes to eat her meals when I do, as its a bonding behavior for parrots, too.
African greys do great with food they can forage and shred... Chance likes carrots and snap peas, especially. Lettuce and leafy greens are great. She does not like radishes and won't eat them. She loves apples and pears.
Make sure you give your African Grey fresh vegetables and fruits. Nuts should be reserved as a treat. I personally like to give my CAG oats, they have a good quantity of vitamin B and other minerals.
Training... Chance responds to the clicker, not food, I think because the sound just grabs her attention, not sure, though.