Yes, sucking fingers is definably is an impropor

sucking fingers is definably is an improper table manner. Besides that, try not to let the silverware scratch the plate/bowl, since that will make noise. And sitting straight while we eat is a basic requirement (that is true for both Chinese and western table manner). The western table manner also require push the soup spoon away from you when eating soup. Trying to eat slowly will help too. When eating the main course, cut a bite size of food, put it entirely into the mouth, then cut another piece, never cut all the food up.