My daughter had her name tagged to a "fake topless photo" on Twitter. This has resulted in her trying being severely depressed.

"Do we have any rights to let the school know that we feel they were negligent in not following up and helping our daughter."...YOU are her parents, NOT the school. Schools are there to educate your child,  why would you expect the school be obligated to parent and care for your child on such an issue? You can ask if they have some programs or accomodations that she may be eligible for if she has a medical/phych condition, but I see no negligence on the part of the school under the facts described. That stated, I would encourage BOTH you and your child secure appropriate counseling as your question suggests that some guidance on proper parenting not freinding, accepting and implementing parental responsibiity and dealing with children and thier use and interaction on the internet would be helpful in addition to helping your child deal with the life lessons of dealing with mean people and developing coping skills and self confidence to ignore them.