1. I would think that the ugly duckling was conflicting with the ducks, marsh birds and wooden duck. (However, there is a slight tinge of character vs self in there.)
2. The ugly duckling is called ugly by everyone and is not accepted by anyone. The ugly duckling has a definite lack of self-esteem.
3. The other characters help reinforce the fact that the ugly duckling is "ugly" and different and by doing so, makes the conflict more intense.