How does the character Howard Roark show self-confidence, his self-esteem, and how he lives second-handedly?
A fascinating question, taken all together.
He shows self-confidence and self-esteem in just about all that he does. He is self-sufficient, following his vision of architecture even when it threatens his place at school and earns him few or no business commissions. He follows his self-esteem even when he might starve to death as a result.
He lives second-handedly only reluctantly and intermittently. That's Peter's position in the book. Roark might be seen as living a second hand life when he lets Peter try to build his design.
Also, though I doubt Rand would think so, some of the social interactions might be considered as living second hand, such as his willingness to learn from Cameron, or his appearance in the courtroom. Why listen to the attacks at all, if he is not accepting them as potentially valid?