Is it permissible to benefit from the service of a company that purchases goods online with its credit card, then sells them to me at a 10% increase over their original price, as a service fee?

If the beneficiary pays the amount due to the company before the company pays it on his behalf, then this is a permissible agency for a fee, and the mentioned percentage is known.

However, if the company pays the price of the purchases first and then the beneficiary pays the company, this combines a loan and an agency for a fee, which is impermissible. This is due to the Prophet's (peace and blessings be upon him) prohibition of combining a loan and a sale, because that is a means to usury and eventually leads to it, as the loan here draws a benefit for the lender.

The legitimate method is for the amount to be paid to the company in advance, so that it becomes an agency for a fee, or for the company to purchase the goods for itself and then sell them to the beneficiary after acquiring ownership.