All data stored is encrypted, apart from public keys. The shard of data are 1Mb at most and are stored encrypted and obfuscated. These move around as well.
To access this data then there are 2 mechanisms
1: Physical access (A person hacks into or takes over your computer physically)
2: A close node (the only nodes that know your ip:port are in your routing table) could known what actual chunks you store as the managers record this. To become a close node is not simple and to target a close group is significantly more difficult.
Illegal actions though should be tracked by those charged with doing so. I believe as the network grows over years there may be actions it can take, but these are more likely to be client side apps to check on behaviour.
A really important aspect here is the anonymity works both ways. We the people can report behaviour of this kind without fear of retribution or being recorded. I think a great many people allow crimes as they are in fear of their lives to report it. This is a deep rabbit hole, but it is a new world and there will be many changes. The whistleblower attributes work for everyone to.
To me education, ridding ourselves of propaganda and having the freedom and security to protect our children and others from abuse may be the very thing that will stop more of this than it does to allow it. I certainly hope so.