Is money earned from affiliate marketing for a website that allows payment in installments with interest permissible or impermissible, knowing that the marketer does not know the buyer's payment method, and should one stop this work?

If the products you market on your website are permissible, then there is no harm for you in that work, and you may benefit from what you earn from it. The buyer's payment method does not affect this. The increase in the installment price over the spot price is permissible and is not usury (riba), because time has a share in the price. Selling on credit or in installments differs from usury, as the increase in the sale is in exchange for the commodity, and not merely for the sake of time.