My info may be a bit dated, but accidents were generally only known to CARFAX if there was as police report filed. But I do know that some repairs and insurance claims do make it onto the report. When is was in the insurance industry, there was a database I had access to that participating insurance companies and shops would report information to. I wouldn't be surprised if CARFAX got access at some point. I do know this was not the case as of 2006-2007 as there was a lot of information I could find on a VIN through this database that wasn't on a CARFAX report. It was primarily there to look for signs of possible fraud. And even then it wasn't complete.
As for diminished value claims, when I was in the industry, it was a relatively new thing. A couple of states mandated it but they had a formula for it. For all other states, it's on the claimant/plaintiff to prove such a thing exists and what the value of such a claim is. I recall a dealer trying to claim that and they were unable to prove such a case. Became much more difficult for them when we could show they had other cars on their lot for sale that had prior damage that were being sold for as much as undamaged cars.