We would not usually use the word zero in these ways.
To say you are zero years old makes no sense so that sentence would not be used and instead of saying "I have zero apples." we would say "I have no apples." or "no food."
In normal conversation you will hear the word zero when they are talking about the weather as in: "The temperature today will be 4 degrees above zero.". Also, You hear the word zero in conversation about sports scores as in: "In baseball news, Detroit beat Cleveland today 4 to zero."
So the rule is when you are talking about numbers you use the word zero when it is appropriate but when you are talking about having something or not having anything you use "no or none" instead of zero. ;-)