The buyer paid, but the item hasn't change to the sold listing.

One of the costumer sent me a message that he already paid for the item, but I haven't received any payment on PayPal for already more than 24 hours. The item is also still marked as a not soled item. Does it meant to be like that? Or the costumer is lying about payments?
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The buyer hasn't paid.  They are not sold. You have received a fake email.

 

When you do sell them, you need to change your postage method to special delivery.  Sending a £500 item by standard 1st class post is another easy way to be scammed.  You need a signature, and full insurance cover.