Is it permissible to take money given for introducing someone to a website that sells clothes online and then purchase from it?

As for the money given for referring customers, there is no harm in it, because it falls under the rubric of permissible brokerage. However, regarding sponsorship (kafalah), it is not permissible to take a fee for it, because it is a gratuitous contract, not an exchange, and because guaranteeing for a fee ultimately leads to usury (riba).