Was he mistaken in not striking the thief, or was it excessive kindness? And should he treat people in kind, or with forgiveness? And what about demanding a large sum of money as ransom for the neighbor's son? And what should he generally do in this situation?

Your conduct with the thief, by pardoning him, is an act of chivalry and seeking reward from Allah. Forgiveness increases you in honor, and good character brings you closer to Allah. Punishing the thief is the responsibility of the ruler. If the amount taken through an informal reconciliation session is equal to the value of what was stolen, there is no problem. Anything in excess of that, the questioner does not have the right to take.