Is it obligatory for a girl to ask her friends to delete her pictures and theirs in which their shoulders are uncovered, for fear that someone might imitate her, or for fear of them being leaked via mobile applications?

There is no harm for a woman in wearing a shoulder abaya if it meets the conditions of the Shariah hijab, meaning it does not define or describe the body parts. It is not a condition to cover the shoulders or back with the same head covering. As for the pictures showing the woman's face, given that her face is considered awrah (private) according to the relied-upon opinion, and if she knew that non-mahram men have seen them, then she must request their deletion if that is possible.