Is it permissible to marry a married man who plans to marry a third and a fourth, asks his second wife to look for them, and then advertises in newspapers his desire for a third wife?

Your husband may marry a third and a fourth wife, and he may publish an advertisement describing the wife, provided that this is done through serious platforms. It is not permissible for him to get to know a woman and meet her in her family's home unless he is determined to marry her. If he is not determined, then it is not permissible for him to look at her, due to the manipulation involved, and because the original ruling is the prohibition of looking [at a non-mahram woman] except for the necessity of engagement.