What is the ruling on profiting from advertisements, most of which are permissible, and is it permissible to display advertisements that show part of a woman's body, such as her hair or ears?

It is not permissible for an advertiser to include a picture of a woman's private parts that must be covered in their advertisement. Likewise, it is not permissible for a viewer to intentionally look at such an image; the ruling on looking at a picture of 'awrah (private parts) is the same as the ruling on looking at the 'awrah itself. As for earning money from placing advertisements on websites, it depends on the type of product or service being advertised. If it is permissible, then earning from it is permissible; otherwise, it is not.