"yemek yemek" is a set phrase. If you use the verb "yemek," it normally requires a noun to go with it. Ergo, "To eat/to eat food" are the same :) It is only in some contexts where you already know what is being consumed that you do not have to include a noun with this verb.
"I want to eat any food" doesn't really make sense in English. "I want to eat some food" would be "Biraz yemek yemek istiyorum" or "Herhangi bir yemek yemek istiyorum."