Obviously social media isn't why this girl tragically committed suicide any more than Instagram is why another girl recently died of injuries caused by self-harm. It's the symptom not the cause.
Indeed, we need better measures to help parents & professionals alike. I've known people who have tragically taken their own lives, and more often than not there have been signs, albeit very subtle ones that someone is collapsing inside. Its so important for people to be able to understand when someone is making a cry for help, and of course how to get them to the help they will need.
Back in my day you got to leave the bullies at the school gate. Now, though, it's constantly there in your pocket, in your phone. I can't imagine the pressure that can cause. People on social media also generally only post the happy things, so it can look as though everyone else is having a wonderful time. If you're feeling lonely and isolated it can tip you over the edge.
As you rightly say, bullies can now reach their victims remotely, directly or indirectly. Even a child's own bedroom may not be considered a safe place for victims of bullies any more. This needs more education on why bullying is wrong, how to spot bullying, how children can safely report bullying, but most of all how to deal with it.
I don't think social media companies deal well with inappropriate things posted on their sites- Twitter, I'm looking at you- but then equally they're not here to be the world's censor. Banning it wouldn't change anything. This girl would tragically still have felt so isolated and unhappy that suicide became her choice.
The very nature of social media means that it is almost impossible to monitor without some form of user regulation. For example the estimated average number of Tweets posted per day is in the region of 500 million, that's around 6,000 per second. Even with the best algorithms to spot inappropriate material you'd struggle to pick up even a fraction without the report Tweet function to highlight problem posts. Then you have to adjudicate each report, some of which could be automated but others would require human intervention. Either way it takes a lot of resource & time to achieve this, and they often still fall way short.
Of course banning it wouldn't help, if one of the big names fell, twenty others would shoot up and take over, perhaps with far less scrupulous checks & measures. That's the nature of the internet now, banning networks doesn't really help, and sometimes it makes things just go deeper and darker. The solution is again education, of both parents and children. For children it is about dealing with social networks the way they were originally meant to be, just another means of communication. They should not be used to add validity to one's own life, a 'Like' or 'ReTweet' is not a sign of social success, indeed there is evidence that many are almost just memory muscle clicks, made without much or any thought to the content. But also teaching children to interact firstly in face-to-face situations, leaving social networks for the times when that isn't as possible (many adults could probably do to learn this too).
For parents its not just about waiting for warning signs, changes in behaviour (never easy as children go through their various stages of life), but about regulating their access, keeping an eye on what they may be viewing and ensuring that they don't have excessive use of mobile contracts, credit cards or other means of silently racking up bills. Its far from an easy balance, and far from an exact science, requiring different children to be taught and dealt with in different ways. But it does require the parents to be more active in their children's internet experience, not just leaving them to it. I am not suggesting this was the situation in this case, but it is too easy for parents to just hand their child a internet connected device and be just happy its keeping them quiet.