In "The Scarlet Letter," what does Pearl need, give, and fear? Who would she like to see?

In the most general sense, Pearl needs a "normal" home life.  In particular, she needs an earthly father as Hester herself notes:  "And my child must seek a heavenly father; she shall never know an earthly one!"  Interestly, this proves to be true; when Dimmesdale finally is ready to accept Pearl, he dies.  Throughout the novel, especially at the second Scaffold Scene, Pearl tries to get Dimmesdale to answer her question: "But wilt thou promise," asked Pearl, "to take my hand, and mother's hand, to-morrow noontide?" 

Once Dimmesdale dies, Pearl seems free of her now unattainable desire, and can begin a "normal" life.

Despite her odd nature and need of a father, Pearl does give meaning to Hester's life ... she is the "Pearl of great price." She is Hester's greatest joy and her greatest grief.