Is it obligatory to cover oneself in a private university for girls if they carry mobile phones and are likely to take pictures, and if so, what should we do if the university prevents this covering on the grounds that it is exclusively for girls?

The basic principle is that a woman is not obliged to cover her face among women, and she is not required to cover it merely due to a suspicion of being photographed. If she actually sees someone intending to photograph her, she can cover her face with a niqab or a book, or similar. The person engaging in this bad behavior should be advised gently, and if necessary, threatened with reporting the matter to the authorities.