First of all, I would correct some errors you made (see in red below):
No, it does not mean "I am having food". The verb "to have" has different meanings in English: one of them is "to possess" or "to own". A different meaning is "to eat" or "to drink" (as in "to have lunch", "to have some tea" etc. – it is not about possession, it is about consumption).
In Russian, the verb "иметь" means "to possess", but never "to consume". If you want to say "I’m having food", it would be "я ем" or "я кушаю" (I’m eating), usually you do not need to add "пища" as it is obvious. But there is also a more official expression for "I'm having food": "я принимаю пищу" (lit.: I'm receiving food). But never "имею".
Technically,
Я имею пищу = У меня есть пища = I have food.
Я имел пищу = У меня была пища = I had food.
They mean just the same.
However, the options with "иметь" sound odd and hardly ever used in the colloquial speech (despite being understandable).
The construction "у + noun in genitive (possessor) + есть + noun in nominative (what is being possessed)" is preferrable and widely used.
The verb "иметь" has limited use in modern Russian. Most often it is used when the subject of possession is something abstract:
Эта олимпиада имеет шанс стать лучшей в истории игр. – These olympic games have a chance to become the best in the history of the games. "шанс" (chance) is an abstract thing.
It can be used in technical or scientific language:
Квадрат имеет четыре стороны. – A square has four sides.
Note: in all the examples above the construction with "у" is still possible, but "иметь" makes them sound more formal.
There are some set expressions with "иметь" and abstract nouns: "иметь значение" - to have importance, to be important, to matter (Размер имеет значение. - The size matters.); "иметь смысл" - to make sense (note: we say "to have sense", not "to make sense") etc. (Это не имеет смысла. - This makes no sense.).
However, if you need an imperative construction, "иметь" (it's imperative form is "имей (те)") is the only option you have:
Не имей сто рублей, а имей сто друзей (Do not have 100 roubles, but have 100 friends) - a Russian saying.
Be careful not to use "иметь" when applying to people (like you say "I have a wife" in English). In Russian slang, it can be used as a euphemism for "to have sex with someone"!