Is it permissible to take a profit in exchange for providing a method of purchasing products from an international shopping website, with the buyer's knowledge of the increase over the original product price for this service?

Since you are an agent for the buyer, your commission must be known to him. You should inform him of the percentage increase on the price or the agreed-upon amount. If you haggle with the seller and get a cheaper price, it is not permissible for you to take the difference for yourself without the buyer's knowledge. Honesty must be upheld, and deceit and trickery in dealings must be avoided, for "whoever cheats us is not of us, and cunning and deception are in the Fire."