Is it permissible to place advertisements for a URL shortening company in a forum that contains songs, movies, and earns profit from its visitors, or is this considered an unlawful earning?

The basic principle is the permissibility of earning money from link shortening that advertises permissible things. However, this work may lead to prohibitions, including: exposure to seeing what is unlawful, and encouraging people of falsehood by increasing the value and importance of their website. Therefore, it is better to avoid dealing with such forums.