As a native speaker, i will prefer to say
आओ और खाना खाओ.
Natives tend to use खाना(object) with खाना(verb) together almost every time.
They didnt give as come and eat food
Come and eat
Are they opening a restaurant?
This is frustrating. I can't answer correctly because it won't accept anything without the final | (apparently equivalent to a period).
Duo yohave our location.
We do say आएं और खाना खाएं या आएं और खाएं। Both are right.