"היא אוכלת עוף ולחם."
Translation:She is eating chicken and bread.
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)
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.