>>1
>>2-san's suggestions are a good starting point, but the most important component is
social engineering; if the paedophiles set up and use a perfectly secure network, you won't be able to do anything solely through technical means.
>>2
A botnet
Attacking public sites directly isn't necessarily a good idea, unless you can manage to take control and get a hold of the server logs (to publish them). Some of the public sites might even be honeypots, so attacking them might be counterproductive.
A machine vision component
But then you need to train it with some actual CP, which is illegal to acquire or possess regardless of the motives. Not a good idea unless you work as part of a police force or something.
Vulnerabilities in encryption cyphers such as AES-256 or enough computing power to crack them.
Forget about it. The best you can get is a flaw in the implementation, not in the actual ciphers used.
>>3
Because it supports child abuse, which in turn destroys lives and causes life-long psychological trauma to the affected. Even if it's a public site, the ads serve to pay for more, and in third-world countries a few dollars might be enough to create another victim.