what was Haus fully developed arc? what makes him well characterized?
Hau is characterized by his optimism in the face of difficulties and challenges. He is humble and greets every new face as a friend regardless of how they treat him. Although tropey, his love for simple things like desserts depicts him as a young man with simple, grounded pleasures. He is self-actualized and comfortable as himself, and this shows in his moderate aspirations. Although it seems clear to others he will follow in the footsteps of grandfather Hala, he is content to take his journey at the pace that suits him.
Hau's arc is that he continually has his positivity challenged until he is met with something that genuinely makes him sad: Lillie leaves Alola. While not explicit, there is implication he has a crush on Lillie that is not reciprocated. It is very difficult for him to say goodbye to her. For the first time, he shows sadness and can be seen moping on the pier.
This is Hau's defining character moment. We see him sad, we see him crying, and we see that Hau has feelings and emotions he does not always let out. With Lillie's departure fresh on his heart, he can either relish in his depression or he can continue staying positive and be excited for his friend. Hau stands up, wipes away his tears, and puts on a smile.
Hau's character is a construct of positive attitude. He is meant to illustrate that how you look at things affects how they affect you. Even when it is difficult to do so, Hau seeks optimism.
I first played SuMo in November 2016. You can probably imagine why a character like that would be comforting to an American like me.