Can I say a burrito is a Mexican food ? Or should I use dish instead ?
Can you say
a Mexican food
Food is an uncountable noun. Sticking Mexican in front of it does make it countable. To sum up: Mexican food is uncountable.
Dish is countable. Therefore Mexican dish is countable.
You do not use the indefinite article before uncountable nouns.
Note: I would not call a burrito a Mexican dish, as it is not a meal. I would call it Mexican food, or a type of Mexican food. To be more specific, it is probably Texmex food, which is food eaten in the southwestern United States that is roughly based on Mexican food, but is not like Mexican food found in the interior of Mexico.
Both.
It is food (obviously).
As for dish, it depends:
1a) any container, generally shallow and concave and of porcelain, earthenware, glass, plastic, etc. for serving or holding food
1b) ([pl.]) plates, bowls, saucers, cups, etc., collectively2a) the food in a dish
2b) a particular kind of food, or food prepared in a certain way ⇒ "one's favorite dish"
So I would not call it a "dish" if served in a paper wrapper, but in a restaurant on a plate it could be. This might also have some special preparation with other food or condiments on the side, in which case the combination of items could be referred to as a "dish".
As for article use, it depends on context but I think you would likely say "Mexican food" instead of "a Mexican food", and "a Mexican dish".