Would the translation "how much does my food cost?" be a correct, although rough?
Yes, this sentence can be translated in many ways that weren't considered.
Directly, it means "How many/much" (The question word for amounts/numbers) "the price" "my" "food". So a lot of translations fit perfectly, including yours.
Agree. This English sentence is unclear. Are you wanting to know how much food you have? Or...how much your food costs?