Should I let my 2 year old litter food and utensil everywhere during meal if he does not have good appetite?

I think you should begin early by telling your kid that it is not fine to litter especially food. The sooner you will start, it will be better as these are going to become habits with your child. To increase his appetite you can see his PD who can advice some syrup to enhance his appetite. Children litter food and mess up when they are either not hungry or doesn't like that particular food. You can give a battery operated toy to your kid and distract him from messing up. http://www.huffingtonpost.com/entry/food-fights-throwing-food_b_1557878.html?section=india

No, by allowing her to litter food and utensil, you will be teaching her that it's okay to disrespect food. Instead, at the first hint of her not being interested, take the plate out of her sight and offer at a later time. :)