Why is "she is eating chicken" accepted without an article ( "a" chicken)
while in a previous exercise "he is eating peach" (without "a" ) was not accepted for "הוא אוכל אפרסק" ?
I'm a native speaker of Hebrew and this is a point about English, but I'll try. In English you say "I eat a peach" but "I eat bread", since peaches are countable and bread is not. In Hebrew there is no "a", so no distinction (אני אוכל אפרסק, אני אוכל לחם). Regarding chicken, I think in most contexts of people eating, "chicken" behaves like a non-countable noun - like bread and not like peaches. One typically doesn't eat one whole bird, but pieces that might come from different individual birds.
You're right but when talking about food עוף is always chicken. If you eat a different bird you would specify it's name and not say עוף (אני אוכלת הודו, פרגית ואווז)