User Activity

I sold an item over a month ago. Item was received and buyer left positive feedback. Now the buyer wants a refund and return item.Do I have to refund in this matter?
I shipped an item to a buyer 1 month ago. It would have taken 3-4 days to get there. Today he informs that he was going through his inventory and the item is not there. He now says he didn't receive it. what do I do?