Is the method of purchasing permissible, where a picture of the product is sent to the seller, who then prepares it and creates an invoice that is sent to the buyer, after which an agreement is made with a shipping company to deliver the product and payment is made upon receipt?

This transaction is valid under the rules of brokerage and mediation, provided their Sharia-compliant conditions are met. However, the sale is not valid if the one you named as seller does not already own the commodity, and if the price is not paid to him at the time of the contract. This transaction can be structured as a non-binding promise to buy and sell, with the actual contract taking place when the price is paid or the commodity is received.