Is it permissible to admire pictures of an unveiled Muslim female friend on social media, what is the best way to advise her, and is following her considered a sin?

Mere admiration of a beautiful girl's picture, or following her for beneficial content on social media, is not prohibited as long as it does not lead to religious proscriptions such as infatuation. A believing woman should utilize her time for what benefits her in her religion and worldly life, for time is precious. Admonition is religiously required, and one can use the girl's good qualities as an entry point for advising her to abandon immodest display (tabarruj), and continue the admonition as long as there is hope it will benefit her. If it is highly probable that it will be useless, then it should be abandoned.