It's uncountable. There is a countable alternative, "foodstuff", but that's only used rarely.

As Niall said, it's uncountable. You could say 'an item of food'. You can use it in plural form to refer to different types of food, but it's still uncountable - e.g. 'some foods are very fattening'.

Not usually. 'Food' is usually classed as a 'mass' rather than a 'unit' type of noun. But, as ever, there are exceptions. You might come across an unusual usage eg 'many different foods', 'It was a food I'd never eaten before'. So long as the form fits the rest of the sentence, such examples are not incorrect.