Did you get recorded delivery? Did you ship to the correct address? If the package did disappear you have to give a refund after exhausting efforts to find it. Wait until buyer opens a case for Item Not Received to give yourself time to locate it.
The seller is always responsible for getting the item to the customer. If it gets lost in the mail you are still responsible and will have to refund them.
This is why you always need to send an item with tracking. Without it you can't prove they actually got it.
A bit longer wait would be appropriate.
Yes, you do.
