"She does not want to tell everything she knows."
Translation:Hon vill inte berätta allt hon vet.
Where would one add the addressee in? Hon vill inte berätta allt hon vet för oss?
Yes, if you have an indirect object, i.e. if the person you're telling is mentioned in the sentence, you have för too: Jag berättade för henne I told her.
But if you just 'tell' without saying who you're telling it to, you don't have för either.
Berätta means to tell, while säga means to say. In some contexts they're essentially interchangeable, but in other they're not. Here though, säga is also accepted.
I got the multiple choice version wrong, but assumed that there was a subtle difference between the two that was not the same as in English. Then again maybe there was a different word that was different between the two sentences and I was focused on "berätta" and "säga." If I see this issue again I'll report it as a bug.