Is it permissible for a brother who took his sister's phone after she talked to a foreign (non-mahram) man to keep it, or must he sell it and give her the money?

If the mobile phone belongs to your sister, it is not permissible for you to seize it, use it, or sell it without her consent, unless she is a minor or mentally incompetent and you are her guardian and deem that to be in her best interest. However, if she is mature, you must forbid her from the evil deed. If she does not desist, you must refer her matter to her guardian so that he may prevent her from it, while continuing to advise her and instill in her the fear of Allah.