What is the ruling on profiting from the website ayuwage.com based on its various methods of earning, and is it permissible to invite others to it?

If the advertisement promotes something forbidden, such as gambling, then the money earned from it is unlawful and must be disposed of. This does not affect what was earned from browsing permissible content. As for the presence of immodest images in advertisements or websites, dealing with or browsing them is not prohibited if they are not intentionally sought out, due to the difficulty of avoiding them and their widespread prevalence.