what one financial request does Pip make of Miss. Havisham? What does this request indicate about his character?

I think you might be referring to chapter 44. Pip asks Miss Havisham for money to help Herbert succeed in his business affairs. Pip does not want Herbert to know where the money has come from. This tells us that Pip is maturing. He is thinking beyond himself. He is not so fixated on becoming a gentleman rather than helping a person that he cares about.