Good Riddles

Question: Living I do not exist. Dead I am an inspiration. You always doubt me. But never reject me. I am what is given from old to young. Without me people would not learn mistakes. What am I?

Question: Waking up I see a smile as warm as fire. Sleeping I see a gaze as cold as ice.

Question: Which triangle will have a larger perimeter : 3,4,5 or 3,4,7 ?

Question: A man goes rock climbing and falls. But at the end of the climb, he appears to be fine. What happened?

Question: If you have me, you want to share me. If you share me, you haven't got me. What am I?