Good grief, this is a can of worms. I am a layman, so excuse me if I don't say the right things, but maybe I can supply more information, as this is becoming a big problem.
If you are trying to sum it up as a disorder, I suggest looking at Histrionic Personality Disorder, which is certainly close to the Amanda Todd story.
If you are looking for examples, then try Aurora Eller, Jessi Slaughter and perhaps even Megan Meier.
Reasons? Plenty. After Demi Lovato and others confessed to self-harm, her fans thought it was cool to do so and to broadcast it online. Worse, a group of girls calling themselves the Árianators' decided that it was cool to threaten suicide online after a certain event concerning the release of an Ariana Grande album. If you're looking for overt examples, may I suggest my blog, and in particular chatlogs referring to Amanda Todd's online behaviour, quoting Amanda herself.
http://philipjrose.wordpress.com/2013/04/25/amandas-last-appearance-as-cutiielover/
I would be interested in knowing if there is a connection with Amanda Todd and any increase in this activity. There is a famous picture online that says 'Beware - the copycats are coming'.
Historically, this has been going on for some time now and is only just beginning to get noticed. In case you need some online vocabulary 'heroes' have been trying to deal with this for some time, and met with very little assistance, and, as you say, a lot of enmity both from parents and the children. Being a hero entails tracking various events online and trying to do something about it (in short). Not to be confused with an hero of course.
You may also be interested in the Hannah Smith story and Ask.fm. When the authorities asked for a check, 95% of the abuse came from her laptop - see self-cyber-bullying.
As far as trying to call it a mental illness, well that's a doozy. The only solution would seem to be denying Internet access, but then the kids go crazy and threaten suicide. In the UK, it was suggested that Hannah Smith (seriously) was suffering from PTSD after phone confiscation. One of the commenters hit it close by saying it's a behavioural problem. Whose responsibility is that? YouTube and Facebook need to be very much on the ball, and I guess you already know about Omegle etc. I have hinted at Histrionic Personality Disorder, but I'm not sure.
One of your commenters mentioned pedophiles and predators. Beware - a lot of that is simply untrue, and is used to try and explain things in more acceptable terms - people simply don't want to come to terms with the fact that young girls are going online and soliciting responses without any coercion or encouragement. Another thing to watch out for is alcohol and marijuana - both lower inhibitions, and are factors in online behaviour (Aurora Eller's father suppled beer; Amanda Todd smoked weed).
Low self-esteem? Well, I don't think so. In fact, I would argue perhaps the opposite. Amanda Todd in particular adored the attention (until it all went wrong). She could not resist the lure of the Internet, posting videos of herself singing, taking drugs, the works. Not exactly a low-esteem shrinking violet, and I think this thing of 'looking for love' is a red herring.
Miley Cyrus Syndrome? Well, almost definitely.
Cops? Forget it. They would be inundated, and have no clue about how to deal with it. Amanda Todd simply cooked up a pack of lies to cover her actions, as do most of the other kids.
Doctors? Equally useless.
Parents? Don't get me started. Fingers have been pointed at Aurora Eller's dad; Jessi Slaughter's father is an internet legend.
We are in a totally new digital world. More positively, I have noticed one thing - there was an upward trend in online activity like this but kids are quite good at sort of healing themselves. Slowly but surely, self-harm, suicide ideation and online exhibitionism are on the wane - after all, if everyone's doing it, it's no longer special. However, the most impressionable age group - 11 to 12 year olds - are most in trouble. They are shown the Amanda Todd video at school, and believe you me that's not wise. However, I'm wandering off topic. All I can say is - I hope in some way I've helped.