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: Nathan has math 4 times a week. If he has math 8:00 Monday, 9:20 on Tuesday, 10:40 on Wednesday, and 1:20 on Friday, when does Nathan have math on Thursday?

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