Do journals need to save all publication-relevant communications
Journals do not have any legal obligation to store all documents associated with the review process. While many do store them in the electronic system, these systems are still relatively new. I have never heard discussions about record archiving polocies. Further, when journals switch review systems, the records are sometimes lost.

Of course, you have access to all these documents, and should use whatever archiving policy you think is relevant. I tend to save all the documents. I have paper files for my older manuscripts and purely electronic files for newer manuscripts.