Facts to their immunity? Yes I do. Here you go -
https://www.law.cornell.edu/uscode/text/42/300aa-22
Actual harm done? Come on. You have brain just like me. There wouldn’t be a Vaccine Injury Trust Fund if there weren’t injuries! That’s an actual government agency for, wait for it, vaccine injuries. So yes there wouldn’t be this agency if there wasn’t actual harm being done. And there’s no science to refute there, the agency really does exist.