What is the ruling on advertising my website—the entire content of which I do not know whether it is permissible or impermissible—through another website, knowing that I pay for that? And is it permissible to advertise and pay other websites that contain both the permissible and the impermissible?

There is no objection to promoting your website through other websites that contain religious violations, as long as your website's content is permissible and is promoted in a permissible way. There is no objection to paying money for the promotion service, because the intention is to promote your permissible website content, not to assist them in publishing forbidden content.