"Setting the table" means laying out the plates and utensils. It might also include setting out the table cloth, setting out any center piece to be used, etc., depending on the formality of the meal being prepared for. It does not include bringing food to the table.
The act of bringing the food to the table is called "serving the meal".
Do we have to say “set the table and then set food on the table for dinner”?
You can say, "set the table and then serve dinner".
In Asia, people in a family share food, they don’t divide food into portions.
English idioms are generally geared toward the cultural practices of the English speaking world, rather than to the practices in Asia, so this fact does not bear strongly on how the preparations for a meal are described in English. Indian English likely has idioms suitable for the practices in South Asia, but these may also be quite different from what's done in East Asia.