What are the major instance in the first 15 chapters where the character notices his or her reflection? What do we learn bout that character in that scene?

Mirror imagery is an important device that Hawthorn uses. It's really everywhere. I can give you two,

"As Hester passes the magnificent artifact of war, the image of her scarlet letter appears in the gleaming metal. Magnified to immense proportions, the burning sign of sin represents Hester's isolation from society. The armor produces only a reflection of her scarlet letter; likewise, the townspeople's image of Hester revolves around her sin."

Hester sees herself in Pearls eyes, "Once their, freakish, elfish cast came into the child's eyes, While Hester was looking at her own image in them...."