What does Pip resolve to do at the end of Chapter LVII (57)? What is the result of his plan?

Pip is committed to returning to the forge and to ask for forgiveness for everything he has done. He also wants to ask Biddy to marry him.

Pip comes to the forge and indeed finds happiness -- but the happiness is Joe and Biddy's. It is their wedding day.Pip wishes them well, truly, and asks them for their forgiveness in all his actions. They happily give it.