Delivery Confirmation shows package Delivered( Ask her/him to check with the people around him/her to see if anyone got the package and forgot to tell the buyer.
2> If you ship via USPS, tell the buyer, delivery confirmation number was scanned at the destination postoffice before putting in delivery truck, ask the buyer take the delivery confirmation number and go to the his/her local post office, he/she may find his/her package there.(package may may still sitting in post office)
3>No, you don't need to 赔偿 unless the buyer purchased insurance or registered service and you failed to do that for her/him.
(when the tracking shows delivered, it really shows you shipped out the package, it is not your fault if the package is not registered or insuranced)