What is the ruling on profiting from "likes" on social media pages that may contain pictures of immodestly dressed women, while disregarding the content? And is it permissible to pay someone to attract visitors to my page, even if the visitor is not interested in the content and "likes" it for a small amount of money, or through illicit methods unknown to me?

What is built upon trickery, deception, and fraud is invalid. This includes hiring someone to record 'likes' and dealing with those who do so or bring someone who does, as it constitutes misrepresentation and deception towards companies. If this is the case, then it is impermissible to do it or earn from it. It has been narrated: "Deceit and treachery are in the Fire." Deception is not befitting for believers, because it contradicts sincerity and affection, and it cultivates sin and transgression.