Is it permissible to advertise for foreign companies that offer permissible services, knowing that their services may be used in impermissible activities, and that they do not differentiate between what is lawful and what is unlawful? What if these companies publish achievements on their website that may include impermissible acts? And is it permissible to advertise if their website designer publishes his achievements, which may include Sharia violations?

There is no harm in advertising permissible things and earning a fee for it. It is permissible to advertise for companies that deal in both permissible and impermissible matters, as long as their dealings are not predominantly impermissible. There is no harm in displaying pictures of previous works if they were permissible. As for impermissible work, it is not permissible to display it. If the display includes both permissible and forbidden elements, and it is possible to control the display of the permissible parts, then there is no harm. There is no harm in displaying a link to the company's website if most of its content is permissible, and the presence of some forbidden images does not affect this, because such things have become widespread [and difficult to avoid entirely]. The person entering the website should fear Allah and avoid forbidden things.