What is the ruling on earning profit from marketing a product that is Islamically permissible, at a known percentage upon purchase, or earning profit from another product that was not promoted when clicking on the displayed product link, or earning profit from the number of clicks on a permissible product even if it is not purchased, knowing that the website earns from advertisements and prohibited products? Is the profit mixed?

There is no harm in earning from marketing commissions for permissible products, whether the commission is for purchasing the product through your link, or purchasing another product after accessing it through the link, or even merely for a certain number of people visiting the link. The mixing of the website's money with unlawful gains does not affect the permissibility of this transaction as long as it is permissible, due to the permissibility of dealing with mixed wealth, as the Companions did with the Jews.